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BEGIN:VEVENT
SUMMARY:Cihan Okay (Bilkent University)
DTSTART:20201005T104000Z
DTEND:20201005T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/1
DESCRIPTION:Title: Commutative $d$-torsion $K$-theory and its applications\nby Ciha
n Okay (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SB-Z11.\n\nAbstract\nCommutative $K$-theory is introduced by Adem
-Gomez-Lind-Tillmann as a generalized cohomology theory obtained from topo
logical $K$-theory. The construction uses classifying spaces for commutati
vity\, first introduced by Adem-Cohen-Torres Giese. In this talk we are in
terested in a $d$-torsion version of this construction: Let $G$ be a topol
ogical group. The aforementioned classifying space $B(\\mathbb{Z}/d\,G)$ i
s assembled from tuples of pairwise commuting elements in $G$ whose order
divides $d$. We will describe the homotopy type of this space when $G$ is
the stable unitary group\, following the ideas of Gritschacher-Hausmann. T
he corresponding generalized cohomology theory will be called the commutat
ive $d$-torsion $K$-theory\, and will be denoted by $k\\mu_d$. Our motivat
ion for studying this cohomology theory comes from applications to operato
r-theoretic problems that arise in quantum information theory. For this we
introduce another spectrum obtained from $k\\mu_d$ and show that a famous
construction from the study of quantum contextuality\, known as Mermin's
square\, corresponds to a non-trivial class in this generalized cohomology
theory. This refines the topological approach to quantum contextuality de
veloped earlier jointly with Raussendorf.\n\nFor a related talk see https:
//www.youtube.com/watch?v=XCTHaASjurg\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Surojit Ghosh (University of Haifa)
DTSTART:20201019T104000Z
DTEND:20201019T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/2
DESCRIPTION:Title: Higher differentials in Adams spectral sequence\nby Surojit Ghos
h (University of Haifa) as part of Bilkent Topology Seminar\n\nLecture hel
d in SB-Z11.\n\nAbstract\nThe $E_2$-term of the Adams spectral sequence ma
y be identified with certain derived functors\, and this also holds for ot
her Bousfield-Kan types spectral sequence.\n\nIn this talk\, I'll explain
how the higher terms of such spectral sequences are determined by truncati
ons of functors\, defined in terms of certain (spectrally) enriched functo
r called mapping algebras.\n\nThis is joint work with David Blanc.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Díaz Ramos (Universidad de Málaga)
DTSTART:20201026T104000Z
DTEND:20201026T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/3
DESCRIPTION:Title: On Quillen’s conjecture\nby Antonio Díaz Ramos (Universidad d
e Málaga) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\
n\nAbstract\nQuillen’s conjecture relates an algebraic invariant and a h
omotopy invariant of a finite group. The conjecture is known to hold for s
everal families of groups since the work of Quillen\, Aschbacher\, Smith a
nd Alperin in the 80’s and 90’s. Here we present a new geometric appro
ach to the subject.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Gritschacher (University of Copenhagen)
DTSTART:20201102T104000Z
DTEND:20201102T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/4
DESCRIPTION:Title: On the space of commuting $n$-tuples in a Lie group\nby Simon Gr
itschacher (University of Copenhagen) as part of Bilkent Topology Seminar\
n\nLecture held in SB-Z11.\n\nAbstract\nThe space of $n$-tuples of pairwis
e commuting elements in a compact Lie group $G$ can be identified with a m
oduli space of flat $G$-bundles over the $n$-torus. Borel\, Friedman\, and
Morgan studied spaces of commuting pairs and triples to answer questions
arising in mathematical physics. Often the focus lies on the enumeration o
f connected components\, but little is known about their higher homotopy a
nd homology groups. In this talk I will describe the second homology group
of the space of commuting pairs in any connected Lie group. Some results
about about $n$-tuples for $n>2$ in groups of type A or C are also obtaine
d. This is joint work with Alejandro Adem and Jose Manuel Gomez.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Adem (University of British Columbia)
DTSTART:20201116T150000Z
DTEND:20201116T155000Z
DTSTAMP:20260424T221812Z
UID:BilTop/5
DESCRIPTION:Title: Free Finite Group Actions on Rational Homology Spheres\nby Aleja
ndro Adem (University of British Columbia) as part of Bilkent Topology Sem
inar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk we will describe
joint work with Ian Hambleton on finite group actions on rational homolog
y 3-spheres\, focusing on the case of untwisted actions. Applications to h
yperbolic manifolds and possible extensions to higher dimensional manifold
s will also be discussed. Several examples will be provided.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Williams (University of British Columbia)
DTSTART:20201207T154000Z
DTEND:20201207T163000Z
DTSTAMP:20260424T221812Z
UID:BilTop/6
DESCRIPTION:Title: A1 homotopy groups of GL_n and a problem of Suslin's\nby Ben Wil
liams (University of British Columbia) as part of Bilkent Topology Seminar
\n\nLecture held in SB-Z11.\n\nAbstract\nLet $F$ be an infinite field. And
rei Suslin constructed a morphism from the (Quillen) K-theory of $F$ to th
e Milnor K-theory of $F$: $s_n : K_n(F) \\to K_n^M(F)$. He proved that the
image of $s_n$ contains $(n-1)! K_n^M(F)$. He raised the question of whet
her this accounted for the whole image—it was known to when $n$ is $1$\,
$2$ or $3$. In this talk I will explain how one can partially recover thi
s morphism as a morphism of $A^1$-homotopy groups of down-to-earth objects
\, and I will show how this tells us some things about Suslin's question w
hen $n$ is $4$ and settles it when $n$ is $5$. This talk represents joint
work with Aravind Asok and Jean Fasel.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aslı Güçlükan (Dokuz Eylul University)
DTSTART:20201012T104000Z
DTEND:20201012T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/7
DESCRIPTION:Title: Small covers over a product of simplices\nby Aslı Güçlükan (
Dokuz Eylul University) as part of Bilkent Topology Seminar\n\nLecture hel
d in SB-Z11.\n\nAbstract\nChoi shows that there is a bijection between Dav
is–Januszkiewicz equivalence classes of small covers over an $n$-cube an
d the set of acyclic digraphs with $n$-labeled vertices. Using this\, one
can obtain a bijection between weakly $(\\mathbb{Z}/2)^n$-equivariant home
omorphism classes of small covers over an $n$-cube and the isomorphism cla
sses of acyclic digraphs on labeled $n$ vertices up to local complementati
on and reordering vertices. To generalize these results to small covers o
ver a product of simplices we introduce the notion of $\\omega$-weighted d
igraphs for a given dimension function $\\omega$. It turns out that there
is a bijection between Davis–Januszkiewicz equivalence classes of small
covers over a product of simplices and the set of acyclic $\\omega$-weight
ed digraphs. After introducing the notion of an $\\omega$-equivalence\, we
also show that there is a bijection between the weakly $(\\mathbb{Z}/2)^n
$-equivariant homeomorphism classes of small covers over $\\Delta^{n_1}\\
times\\cdots \\times \\Delta^{n_k}$ and the set of $\\omega$-equivalence c
lasses of $\\omega$-weighted digraphs with $k$-labeled vertices $\\{v_1\,
\\cdots\, v_k\\}$ where $\\omega$ is defined by $\\omega(v_i)=n_i$ and $n=
n_1+\\cdots+n_k$. As an example\, we obtain a formula for the number of we
akly $(\\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers
over a product of three simplices.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akhil Mathew (University of Chicago)
DTSTART:20201214T154000Z
DTEND:20201214T163000Z
DTSTAMP:20260424T221812Z
UID:BilTop/8
DESCRIPTION:Title: Descent and vanishing in algebraic K-theory via group actions\nb
y Akhil Mathew (University of Chicago) as part of Bilkent Topology Seminar
\n\nLecture held in SB-Z11.\n\nAbstract\nI will explain some descent and v
anishing results in the\nalgebraic K-theory of ring spectra\, motivated by
the redshift\nphilosophy of Ausoni-Rognes. These results are all proved b
y\nconsidering group actions on stable $\\infty$-categories and their\nK-t
heory\, as well as some tools coming from chromatic homotopy theory.\nJoin
t work with Dustin Clausen\, Niko Naumann\, and Justin Noel.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernardo Villarreal (National Autonomous University of Mexico)
DTSTART:20201130T140000Z
DTEND:20201130T145000Z
DTSTAMP:20260424T221812Z
UID:BilTop/9
DESCRIPTION:Title: A Lie group analogue of the coset poset of abelian subgroups\nby
Bernardo Villarreal (National Autonomous University of Mexico) as part of
Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nTo a gro
up G and a family of subgroups F\, one can associate a simplicial complex
C(F\,G)\, whose simplices are in correspondence with the chains of cosets
of G\, with respect to F. Abels and Holz studied some homotopy properties
of C(F\,G)\, and their relationship with G. For example\, C(F\,G) is simpl
y-connected if and only if G is the amalgamated product of subgroups in F
along its intersections. C. Okay noted that for an arbitrary group G\, spe
cializing the simple-connectivity of C(F\,G) to the family of abelian subg
roups\, forces G to be abelian.\n\nIn this talk I will discuss a Lie group
analogue of C(F\,G) with respect to the family of abelian subgroups\, ari
sing from the work of Adem\, Cohen and Torres-Giese. The main result I wil
l describe is recent work with O. Antolín-Camarena and S. Gritschacher wh
ich deals with the analogue of Okay’s result for compact Lie groups.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sumeyra Sakalli (Max Planck Institute for Mathematics)
DTSTART:20201221T104000Z
DTEND:20201221T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/10
DESCRIPTION:Title: Exotic 4-Manifold Constructions via Pencils of Curves of Small Gen
us and Surgeries\nby Sumeyra Sakalli (Max Planck Institute for Mathema
tics) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAb
stract\nExotic manifolds are smooth manifolds which are homeomorphic but n
ot\ndiffeomorphic to each other. Constructing exotic manifolds in dimensio
n\nfour has been an active research area in low dimensional and symplectic
\ntopology over the last 30 years. In this talk\, we will first discuss ma
jor\nopen problems and some recent progress in 4-manifolds theory. Then we
\nwill discuss our constructions of exotic 4-manifolds via pencils of comp
lex\ncurves of small genus and via symplectic and smooth surgeries. Some o
f\nour results that will be presented are joint with A. Akhmedov.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozgur Bayindir (University of Paris 13)
DTSTART:20201123T104000Z
DTEND:20201123T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/11
DESCRIPTION:Title: Algebraic $K$-theory of $THH(\\mathbb{F}_p)$\nby Ozgur Bayindir
(University of Paris 13) as part of Bilkent Topology Seminar\n\nLecture h
eld in SB-Z11.\n\nAbstract\nIn this work\, we study $THH(\\mathbb{F}_p)$ f
rom various perspectives. We\nstart with a new identification of $THH(\\ma
thbb{F}_p)$ as an $E_2$-algebra.\nFollowing this\, we compute the $K$-theo
ry of $THH(\\mathbb{F}_p)$.\n\nThe first part of my talk is going to consi
st of an introduction to\nalgebraic $K$-theory and the Nikolaus Scholze ap
proach to trace methods.\nIn the second part\, I will introduce our result
s and the tools we\ndevelop to study the topological Hochschild homology o
f graded ring\nspectra and formal differential graded algebras.\n\nThis is
a joint work with Tasos Moulinos.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20210208T103000Z
DTEND:20210208T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/12
DESCRIPTION:Title: The Dade group of a finite group and dimension functions\nby Er
gun Yalcin (Bilkent University) as part of Bilkent Topology Seminar\n\nLec
ture held in SB-Z11.\n\nAbstract\nIf $G$ is a $p$-group and $k$ is a field
of characteristic $p$\, then the Dade group $D(G)$ of $G$ \nis the group
whose elements are the equivalence classes of capped endo-permutation $kG$
-modules\, \nwhere the group operation is given by the tensor product over
$k$. The Dade groups of p-groups have been \nstudied intensively in the l
ast 20 years\, and a complete description of the group $D(G)$ has been \ng
iven by Bouc in terms of the genetic sections of $G$.\n\nFor finite groups
the situation is more complicated. There are two definitions of a Dade gr
oup of a finite\ngroup given by Urfer and Lassueur\, however both definiti
ons have some shortcomings. In a recent work \nwith Gelvin\, we give a new
definition for the Dade group $D(G)$ of a finite group $G$ by introducing
a notion \nof Dade $kG$-module as a generalization of endo-permutation mo
dules.\n \n\nWe show that there is a well-defined surjective group homomor
phism $\\Psi$ from the group of super class \nfunctions $C(G\, p)$ to the
Dade group $D^{\\Omega} (G)$ generated by relative syzygies. Our main theo
rem \nis the verification that the subgroup of $C(G\,p)$ consisting of the
dimension functions of k-orientable real representations \nof $G$ lies in
the kernel of $\\Psi_G$. In the proof we consider Moore $G$-spaces which
are the equivariant versions \nof spaces which have nonzero reduced homolo
gy in only one dimension\, and use the techniques \nfrom homological algeb
ra over the orbit category.\n \n\nThis is a joint work with Matthew Gelvin
.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ran Levi (University of Aberdeen)
DTSTART:20210215T103000Z
DTEND:20210215T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/13
DESCRIPTION:Title: An application of neighbourhoods in directed graphs in the classifi
cation of binary dynamics\nby Ran Levi (University of Aberdeen) as par
t of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nA bi
nary state on a graph means an assignment of binary values to its vertices
. For example\, if one encodes a network of spiking neurons as a directed
graph\, then the spikes produced by the neurons at an instant of time is a
binary state on the encoding graph. Allowing time to vary and recording
the spiking patterns of the neurons in the network produces an example of
a binary dynamics on the encoding graph\, namely a one-parameter family
of binary states on it. The central object of study in this talk is the ne
ighbourhood of a vertex $v$ in a graph $\\mathcal{G}$\, namely the subgrap
h of $\\mathcal{G}$ that is generated by $v$ and all its direct neighbours
in $\\mathcal{G}$. We present a topological/graph theoretic method for e
xtracting information out of binary dynamics on a graph\, based on a selec
tion of a relatively small number of vertices and their neighbourhoods. As
a test case we demonstrate an application of the method to binary dynamic
s that arises from sample activity on the Blue Brain Project reconstructio
n of cortical tissue of a rat.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calista Bernard (Stanford University)
DTSTART:20210308T103000Z
DTEND:20210308T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/14
DESCRIPTION:Title: Twisted homology operations\nby Calista Bernard (Stanford Unive
rsity) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nA
bstract\nIn the 70s\, Fred Cohen and Peter May gave a description of the m
od $p$ homology of a free $E_n$-algebra in terms of certain homology opera
tions\, known as Dyer--Lashof operations\, and the Browder bracket. These
operations capture the failure of the $E_n$ multiplication to be strictly
commutative\, and they prove useful for computations. After reviewing the
main ideas from May and Cohen's work\, I will discuss a framework to gener
alize these operations to homology with certain twisted coefficient system
s and give a complete classification of twisted operations for $E_{\\infty
}$-algebras. I will also explain computational results that show the exist
ence of new operations for $E_2$-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Yiu Chung (University of Southampton)
DTSTART:20210315T103000Z
DTEND:20210315T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/15
DESCRIPTION:Title: Bieberbach group and decomposing flat manifolds\nby Ho Yiu Chun
g (University of Southampton) as part of Bilkent Topology Seminar\n\nLectu
re held in SB-Z11.\n\nAbstract\nAn n-dimensional Bieberbach group is a dis
crete\, cocompact torsion-free subgroup of the group of isometries of Eucl
idean n-space. In this talk\, we will introduce the three Bieberbach theor
ems in order to understand the algebraic structure of Bieberbach groups. S
uch groups are interesting because they arise as fundamental group of comp
act flat Riemannian manifolds. In the second half of the talk\, we will di
scuss the Vasquez invariant of finite groups which was introduced by A. T.
Vasquez in 1970. This invariant is related to a decomposition theorem of
sorts for compact flat Riemannian manifolds. We will discuss several resul
ts about such invariant.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20210322T103000Z
DTEND:20210322T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/16
DESCRIPTION:Title: Higher order Toda brackets\nby Aziz Kharoof (University of Haif
a) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstr
act\nToda brackets are a type of higher homotopy operation. Like Massey pr
oducts\, they are not always defined\, and their value is indeterminate. N
evertheless\, they play an important role in algebraic topology and relate
d fields:
Toda originally constructed them as a tool for
computing homotopy groups of spheres. Adams later showed that they can be
used to calculate differentials in spectral sequences.\n\nAfter reviewing
the construction and properties of the classical Toda bracket\, we shall
describe a higher order version\, there are two ways to do that. We will p
rovide a diagrammatic description for the system we need to define the hig
her order Toda brackets\, then we will use that to give alternative defini
tion using the homotopy cofiber.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Sanchez Ocal (Texas A&M University)
DTSTART:20210329T103000Z
DTEND:20210329T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/17
DESCRIPTION:Title: Hochschild cohomology of general twisted tensor products\nby Pa
blo Sanchez Ocal (Texas A&M University) as part of Bilkent Topology Semina
r\n\nLecture held in SB-Z11.\n\nAbstract\nThe Hochschild cohomology is a t
ool for studying associative algebras that has a lot of structure: it is a
Gerstenhaber algebra. This structure is useful because of its application
s in deformation and representation theory\, and recently in quantum symme
tries. Unfortunately\, computing it remains a notoriously difficult task.
In this talk we will present techniques that give explicit formulas of the
Gerstenhaber algebra structure for general twisted tensor product algebra
s. This will include an unpretentious introduction to this cohomology and
to our objects of interest\, as well as the unexpected generality of the t
echniques. This is joint work with Tekin Karadag\, Dustin McPhate\, Tolulo
pe Oke\, and Sarah Witherspoon.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atabey Kaygun (Istanbul Technical University)
DTSTART:20210405T103000Z
DTEND:20210405T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/18
DESCRIPTION:Title: From filtered complexes to matroids to cobordisms: an unlikely stor
y in three parts\nby Atabey Kaygun (Istanbul Technical University) as
part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nO
ur story starts with a question in data analysis and computational topolog
y/geometry. Given a finite sample of points from an unknown manifold embed
ded in an affine space\, how can we extract information about topological
invariants of the said manifold? Even though the answer is known for a lon
g time\, the connections of the question with computational geometry and d
ata analysis have only recently been made. We will review these connection
s\, and then move on to the "representation problem" of homology of filter
ed complexes. Specifically\, we will explain why "bar-codes" are enough fo
r filtered complexes over reals\, but why there is no such hope for other
seemingly nice posets. Then we will talk about why matroids and cobordisms
(of spheres) might naturally provide us the necessary tools for devising
a solution for this problem.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rune Haugseng (Norwegien University of Science and Technology)
DTSTART:20210412T103000Z
DTEND:20210412T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/19
DESCRIPTION:Title: Higher Morita categories\nby Rune Haugseng (Norwegien Universit
y of Science and Technology) as part of Bilkent Topology Seminar\n\nLectur
e held in SB-Z11.\n\nAbstract\nClassical Morita theory for associative alg
ebras can be described in terms of a 2-category with associative algebras
as objects\, bimodules as morphisms\, and bimodule homomorphisms as 2-morp
hisms\; this can be further enhanced to a double category that also includ
es algebra homomorphisms. More generally\, we can consider 2-categories an
d double categories of enriched categories and bimodules between them. I w
ill discuss homotopical versions of these structures and their higher-dime
nsional generalizations to $E_n$-algebras and enriched n-categories\, whic
h are of interest as targets for fully extended TQFTs.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Scoccola (Michigan State University)
DTSTART:20210419T123000Z
DTEND:20210419T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/20
DESCRIPTION:Title: Approximate and discrete vector bundles in theory and applications<
/a>\nby Luis Scoccola (Michigan State University) as part of Bilkent Topol
ogy Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nSynchronization proble
ms\, such as the problem of reconstructing a 3D shape from a set of 2D pro
jections\, can often be modeled by principal bundles. Similarly\, the appl
ication of local PCA to a point cloud concentrated around a manifold appro
ximates the tangent bundle of the manifold. In the first case\, the charac
teristic classes of the bundle provide obstructions to global synchronizat
ion\, while\, in the second case\, they provide topological information of
the manifold beyond its homology\, and give obstructions to dimensionalit
y reduction. I will describe joint work with Jose Perea in which we propos
e notions of approximate and discrete vector bundle\, study the extent to
which they determine true vector bundles\, and give algorithms for the sta
ble and consistent computation of low-dimensional characteristic classes d
irectly from these combinatorial representations.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Romero (Universidad de la Rioja)
DTSTART:20210503T103000Z
DTEND:20210503T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/21
DESCRIPTION:Title: Effective homology and perturbation theory for computations in alge
braic topology\nby Ana Romero (Universidad de la Rioja) as part of Bil
kent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk
we will present the theory of effective homology\, a technique which can
be used for computing homology and homotopy groups of complicated spaces.
We will also present some perturbation lemmas\, which are the main ingredi
ent to determine the effective homology of many spaces. Both techniques ar
e implemented in the computer algebra system Kenzo\, which has made it pos
sible to determine homology and homotopy groups of spaces of infinite type
. We will finish the talk with some examples of calculations.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART:20210301T133000Z
DTEND:20210301T143000Z
DTSTAMP:20260424T221812Z
UID:BilTop/22
DESCRIPTION:Title: Variants of the Waldhausen S-construction\nby Julie Bergner (Un
iversity of Virginia) as part of Bilkent Topology Seminar\n\nLecture held
in SB-Z11.\n\nAbstract\nThe S-construction\, first defined in the setting
of cofibration categories by Waldhausen\, gives a way to define the algebr
aic K-theory associated to certain kinds of categorical input. It was pro
ved by Galvez-Carrillo\, Kock\, and Tonks that the result of applying this
construction to an exact category is a decomposition space\, also called
a 2-Segal space\, and Dyckerhoff and Kapranov independently proved the sam
e result for the slightly more general input of proto-exact categories. I
n joint work with Osorno\, Ozornova\, Rovelli\, and Scheimbauer\, we prove
d that these results can be maximally generalized to the input of augmente
d stable double Segal spaces\, so that the S-construction defines an equiv
alence of homotopy theories. In this talk\, we'll review the S-constructi
on and the reasoning behind these stages of generalization. Time permitti
ng\, we'll discuss attempts to characterize those augmented stable double
Segal spaces that correspond to cyclic spaces\, which is work in progress
with Walker Stern.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozgun Unlu (Bilkent University)
DTSTART:20210222T103000Z
DTEND:20210222T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/23
DESCRIPTION:Title: Free Group Actions on Products of Two Equidimensional Spheres\n
by Ozgun Unlu (Bilkent University) as part of Bilkent Topology Seminar\n\n
Lecture held in SB-Z11.\n\nAbstract\nWe will first review some known restr
ictions on finite groups that can act freely on products of two equidimens
ional spheres. Then we will discuss some constructions of free actions of
finite p-groups on products of two equidimensional spheres. Finally\, we
will discuss some open problems about free $p$-group actions on two equidi
mensional spheres.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Baker (University of Glasgow)
DTSTART:20210426T103000Z
DTEND:20210426T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/24
DESCRIPTION:Title: Duals of P-algebras and their comodules\nby Andrew Baker (Unive
rsity of Glasgow) as part of Bilkent Topology Seminar\n\nLecture held in S
B-Z11.\n\nAbstract\nP-algebras are connected graded cocommutative Hopf alg
ebras which are unions of finite dimensional Hopf algebras (which are also
Poincare duality algebras). These are quasi-Frobenius algebras and have s
ome remarkable homological properties. The motivating examples for which t
he theory was produced are the Steenrod algebra at a prime and large sub a
nd quotient \nHopf algebras. \n\nThe dual of a P-algebra is a commutative
Hopf algebra and I will discuss some homological properties of its comodul
es. In particular there is a large class of coherent comodules which admit
finitely generated projective resolutions\, but finite dimensional comodu
les have no non-trivial maps from these. \n\nUsing some Cartan-Eilenberg s
pectral sequences this can be applied to show that certain Bousfield class
es of spectra are distinct\, thus extending results of Ravenel.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (University of Warwick)
DTSTART:20211004T103000Z
DTEND:20211004T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/25
DESCRIPTION:Title: $RO(C_2)$-graded coefficients of $C_2$-Eilenberg-MacLane spectra\nby Igor Sikora (University of Warwick) as part of Bilkent Topology Semi
nar\n\nLecture held in SB-Z11.\n\nAbstract\nIn non-equivariant topology th
e ordinary homology of a point is described by the dimension axiom and is
quite simple - namely\, it is concentrated in degree zero. The situation i
n $G$-equivariant topology is different. This is due to the fact that Bred
on homology - the equivariant counterpart of the ordinary homology - is na
turally graded over $RO(G)$\, the ring of $G$-representations. Whereas the
equivariant dimension axiom describes the part of the Bredon homology of
a point which is graded over trivial representations\, it does not put any
requirements on the rest of the grading - in which the homology may be qu
ite complicated.\n\nThe $RO(G)$-graded Bredon homology theories are repres
ented by $G$-Eilenberg-MacLane spectra\, and thus the Bredon homology of a
point is the same thing as coefficients of these spectra. During the talk
I will present the method of computing the $RO(C_2)$-graded coefficients
of $C_2$-Eilenberg-MacLane spectra based on the Tate square. As demonstrat
ed by Greenlees\, the Tate square gives an algorithmic approach to computi
ng the coefficients of equivariant spectra. In the talk we will discuss ho
w to use this method to obtain the $RO(C_2)$-graded coefficients of a $C_2
$-Eilenberg-MacLane spectrum as a $RO(C_2)$-graded abelian group. We will
also present the multiplicative structure of the $C_2$-Eilenberg-MacLane s
pectrum associated to the Burnside Mackey functor. This allows us to furth
er describe the $RO(C_2)$-graded coefficients of any $C_2$-Eilenberg-MacLa
ne spectrum as a module over the coefficients of the $C_2$-Eilenberg-MacLa
ne spectrum of the Burnside Mackey functor. Finally\, we will discuss the
$RO(C_2)$-graded ring structure of coefficients of spectra associated to r
ing Mackey functors.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tane Vergili (Karadeniz Technical University)
DTSTART:20211011T123000Z
DTEND:20211011T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/26
DESCRIPTION:Title: Persistence modules and the interleaving distance\nby Tane Verg
ili (Karadeniz Technical University) as part of Bilkent Topology Seminar\n
\nLecture held in SB-Z11.\n\nAbstract\nIn topological data analysis\, a pe
rsistence module is obtained with applying homology with coefficients in s
ome fixed field to the increasing family of topological spaces or complexe
s. The distance between two persistence modules can be measured with the i
nterleaving metric. The collection of persistence modules with the interle
aving metric fails to be a topological space since it is not a set but a c
lass. For this\, one can restrict oneself to the identified sets together
with the topology induced by the interleaving distance in order to study t
heir basic topological properties. In this talk we are going to discuss pe
rsistence modules\, the interleaving distance and the topological properti
es of the considered sets of persistence modules induced by the interleavi
ng distance.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Wu (Hebei Normal University)
DTSTART:20211018T103000Z
DTEND:20211018T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/27
DESCRIPTION:Title: Hypergraph homology and its applications\nby Jie Wu (Hebei Norm
al University) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z
11.\n\nAbstract\nIn practical applications\, hypergraph is considered as t
he most general mathematical model for network beyond pairwise interaction
s. From topological views\, the notion of hypergraph is a generalization o
f simplicial complex. In this talk\, we will explain how to naturally exte
nd simplicial homology theory to a homology theory on hypergraphs so that
algebraic topology admits broader applications in practice. As application
s in data science\, we will present hypergraph-based persistent cohomology
(HPC) for molecular representations in drug design.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osman Berat Okutan (Florida State University)
DTSTART:20211025T123000Z
DTEND:20211025T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/28
DESCRIPTION:Title: Persistent Homology and Injectivity\nby Osman Berat Okutan (Flo
rida State University) as part of Bilkent Topology Seminar\n\nLecture held
in SB-Z11.\n\nAbstract\nPersistent homology induced by the simplicial Vie
toris-Rips filtration is a standard method for capturing topological infor
mation from metric spaces. In this talk\, I will describe a more geometric
filtration\, obtained through injective metric spaces\, which is equivale
nt to the Vietoris-Rips filtration up to homotopy. Injective metric spaces
are the injective objects in the category of metric spaces. This new filt
ration allows one to see new connections between the geometry and topology
of the underlying space. This is a joint work with Sunhyuk Lim and Facund
o Memoli.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (Norwegian University of Science and Technology)
DTSTART:20211115T103000Z
DTEND:20211115T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/29
DESCRIPTION:Title: Trigraded spectral sequences for principal fibrations\nby Marku
s Szymik (Norwegian University of Science and Technology) as part of Bilke
nt Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThe Leray--Ser
re and the Eilenberg--Moore spectral sequence are fundamental tools for co
mputing the cohomology of a group or\, more generally\, of a space. In joi
nt work with Frank Neumann\, we describe the relationship between these tw
o spectral sequences in the situation when both of them share the same abu
tment. This talk will be an introduction to the topic and our results with
many examples.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darrick Lee (EPFL)
DTSTART:20211206T103000Z
DTEND:20211206T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/30
DESCRIPTION:Title: A topological approach to signatures\nby Darrick Lee (EPFL) as
part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nT
he path signature is a characterization of paths initially developed by Ch
en to study the topology of loop spaces\, and has recently been used to fo
rm the foundations of rough paths in stochastic analysis\, and provides a
powerful feature map for sequential data in machine learning. In this talk
\, we return to the topological foundations in Chen's iterated integral co
chain models to develop generalizations of the signature.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayse Borat (Bursa Technical University)
DTSTART:20211220T143000Z
DTEND:20211220T153000Z
DTSTAMP:20260424T221812Z
UID:BilTop/31
DESCRIPTION:Title: Simplicial analogues of homotopic distance\nby Ayse Borat (Burs
a Technical University) as part of Bilkent Topology Seminar\n\nLecture hel
d in SB-Z11.\n\nAbstract\nHomotopic distance as introduced by Macias-Virgo
s and Mosquera-Lois in [2]\ncan be realised as a generalisation of topolog
ical complexity (TC) and Lusternik\nSchnirelmann category (cat). In this t
alk\, we will introduce a simplicial analogue of\nhomotopic distance (in t
he sense of Ortiz\, Lara\, Gonzalez and Borat as in [3]) and\nshow that it
has a relation with simplicial complexity (as defined in [1]). We will\na
lso take a glance at contiguity distance - another simplicial analogue of
homotopic\ndistance - as introduced in [2] and improved in [4].\nReference
s\n\n[1] J. Gonzalez\, Simplicial Complexity: Piecewise Linear Motion Plan
ning in Robotics\, New\nYork Journal of Mathematics 24 (2018)\, 279-292.\n
[2] E. Macias-Virgos\, D. Mosquera-Lois\, Homotopic Distance between Maps\
, Mathematical\nProceedings of the Cambridge Philosophical Society (2021)\
, 1-21.\n[3] C. Ortiz\, A. Lara\, J. Gonzalez\, A. Borat\, A randomized gr
eedy algorithm for piecewise linear\nmotion planning\, Mathematics\, Vol 9
\, Issue 19 (2021).\n[4] A. Borat\, M. Pamuk\, T. Vergili\, Contiguity Dis
tance between Simplicial Maps\, submitted\,\n2020. ArXiv: 2012.10627.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Akif Erdal (Yeditepe Universitesi)
DTSTART:20211101T133000Z
DTEND:20211101T143000Z
DTSTAMP:20260424T221812Z
UID:BilTop/32
DESCRIPTION:Title: An Elmendorf-Piacenza type Theorem for Actions of Monoids\nby M
ehmet Akif Erdal (Yeditepe Universitesi) as part of Bilkent Topology Semin
ar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk I will describe a
homotopy theory for actions of monoids that is built by analyzing their ``
reversible parts". Let $M$ be a monoid and $G(M)$ be its group completion.
I will show that the category of $M$-spaces and $M$-equivariant maps admi
ts a model structure in which weak equivalences and fibrations are determi
ned by the standard equivariant homotopy theory of $G(N)$-spaces for each
$N\\leq M$. Then\, I will show that under certain conditions on $M$ this m
odel structure is Quillen equivalent to the projective model structure on
the category of contravariant $\\mathbf{O}(M)$-diagrams of spaces\, where
$\\mathbf{O}(M)$ is the category whose objects are induced orbits $M\\time
s_N G(N)/H$ for each $N\\leq M$ and $H\\leq G(N)$ and morphisms are $M$-eq
uivariant maps. Finally\, if time permits\, I will state some applications
.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer (UT Dallas)
DTSTART:20211108T143000Z
DTEND:20211108T153000Z
DTSTAMP:20260424T221812Z
UID:BilTop/33
DESCRIPTION:Title: Geometric Approaches on Persistent Homology\nby Baris Coskunuze
r (UT Dallas) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z1
1.\n\nAbstract\nPersistent Homology is one of the most important technique
s used in Topological Data Analysis. In the first half of the talk\, we gi
ve an introduction to the subject. In the second half\, we study the persi
stent homology output via geometric topology tools. In particular\, we giv
e a geometric description of the term “persistence”. The talk will be
non-technical\, and accessible to graduate students.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mustafa Korkmaz (METU)
DTSTART:20211129T103000Z
DTEND:20211129T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/34
DESCRIPTION:Title: Involution generators of mapping class groups\nby Mustafa Korkm
az (METU) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n
\nAbstract\nThe mapping class group of a surface plays an important role i
n low \ndimensional topology.\nIts various generating sets are known. Sinc
e it is not a quotient of a \ndihedral group\,\nit cannot be generated by
two involutions. A generating set consisting \nof 4-5 involutions\nhas bee
n known for more than 15 years. In this talk I will show how it \nis gener
ated by 3 involutions.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Castellana (Universitat Autònoma de Barcelona)
DTSTART:20211213T103000Z
DTEND:20211213T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/35
DESCRIPTION:Title: The normalizer decomposition for p-local compact groups\nby Nat
alia Castellana (Universitat Autònoma de Barcelona) as part of Bilkent To
pology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\n(with Eva Belmont\,
Jelena Grbic\, Kathryn Lesh\, Michelle Strumila) In this project we study
the normalizer decomposition of a p-local compact group in a general sett
ing.\nWhen G is a compact Lie group\, using the information of the fusion
system of G on a maximal\ndiscrete p-toral subgroup\, we recover known dec
ompositions in terms of p-centric p-stubborn p-toral\nsubgroups up to p-co
mpletion. But this methods allow to also describe some exotic p-compact gr
oups\nin terms of a pushout.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nima Rasekh (EPFL)
DTSTART:20211122T103000Z
DTEND:20211122T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/36
DESCRIPTION:Title: THH and Shadows of Bicategories\nby Nima Rasekh (EPFL) as part
of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nTopolo
gical Hochschild homology (THH)\, first defined for ring spectra and then
later dg-categories and spectrally enriched categories\, is an important i
nvariant with connections to algebraic K-theory and fixed point methods. T
he existence of THH in such diverse contexts motivated Ponto to introduce
a notion that can encompass the various perspectives: a shadow of bicatego
ries. On the other side\, many versions of THH have been generalized to th
e homotopy coherent setting providing us with motivation to develop an ana
logous homotopy coherent notion of shadows.\n\nThe goal of this talk is to
use an appropriate bicategorical notion of THH to prove that a shadow on
a bicategory is equivalent to a functor out of THH of that bicategory. We
then use this result to give an alternative conceptual understanding of sh
adows as well as an appropriate definition of a homotopy coherent shadow.\
n\nThis is joint work with Kathryn Hess.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Viruel (Universidad de Málaga)
DTSTART:20220221T103000Z
DTEND:20220221T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/37
DESCRIPTION:Title: Path Partial Groups\nby Antonio Viruel (Universidad de Málaga)
as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstrac
t\nIn this lecture we shall show how path concatenation in a simple graph
G gives rise to a partial group P(G) that we call the path partial group a
ssociated to the graph G. The construction of path partial groups is indee
d functorial and allows us to embed the category of simple graphs into the
category of partial groups. This embedding is full on automorphism so it
shows that any group can be realised as the full group of automorphisms of
a partial group\, while not every group is the full group of automorphism
s of an honest group. Finally\, thinking of partial grops as simplicial co
mplexes\, we show that every group is the group of self homotopy equivalen
ces of a simplicial complex. This is a joint work with Antonio Díaz-Ramos
(U. Malaga) and Rémi Molinier (U. Grenoble).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20220228T103000Z
DTEND:20220228T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/38
DESCRIPTION:Title: Higher limits over the fusion orbit category\nby Ergun Yalcin (
Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held in
SB-Z11.\n\nAbstract\nOne of the open problems related to the homotopy the
ory of fusion\nsystems asks whether or not the subgroup decomposition for
a p-local finite\ngroup is sharp. The sharpness of the subgroup decomposit
ion is known to be true\nfor finite group fusion systems\, but in general
this problem is still open except\nfor some special cases. I will describe
some new methods for calculating higher\nlimits over the fusion orbit cat
egory of a discrete group and show how these new\nmethods can be applied t
o the sharpness problem. In particular\, we show that\nthe subgroup decomp
osition for p-local finite groups is sharp\, if it is sharp\nfor every p-l
ocal finite group with nontrivial center.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Adams (Colorado State University)
DTSTART:20220314T103000Z
DTEND:20220314T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/39
DESCRIPTION:Title: An introduction to Vietoris-Rips complexes\nby Henry Adams (Col
orado State University) as part of Bilkent Topology Seminar\n\nLecture hel
d in SB-Z11.\n\nAbstract\nI will give an introduction to Vietoris-Rips com
plexes and their uses in applied and computational topology. If a dataset
is sampled from some unknown underlying space (say a manifold)\, then as m
ore and more samples are drawn\, the Vietoris-Rips persistent homology of
the dataset converges to the Vietoris-Rips persistent homology of the mani
fold. But little is known about Vietoris-Rips complexes of manifolds. An e
xception is the case of the circle: I will describe how as the scale param
eter increases\, the Vietoris-Rips complexes of the circle obtain the homo
topy types of the circle\, the 3-sphere\, the 5-sphere\, ...\, until final
ly they are contractible. Much less is known about Vietoris-Rips complexes
of spheres. I will also briefly explain how Vietoris-Rips complexes relat
e to generalizations of the Borsuk-Ulam theorem and to Gromov-Hausdorff di
stances between spheres.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rick Jardine (Western University)
DTSTART:20220321T133000Z
DTEND:20220321T143000Z
DTSTAMP:20260424T221812Z
UID:BilTop/40
DESCRIPTION:Title: UMAP for the working mathematician\nby Rick Jardine (Western Un
iversity) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n
\nAbstract\nThe Healy-McInnes UMAP algorithm is a highly successful cluste
ring tool that involves interesting ideas from mathematics and data scienc
e:\n\n1) Spivak's theory of extended pseudo metric spaces (ep-metric space
s)\n2) TDA constructions in ep-metric spaces\n3) weighted graphs\n4) class
ical dimension reduction\n5) graph optimization: fuzzy sets\, cross entrop
y\n\nI will explain the algorithm from a mathematical point of view.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toni Annala (University of British Columbia)
DTSTART:20220328T160000Z
DTEND:20220328T170000Z
DTSTAMP:20260424T221812Z
UID:BilTop/41
DESCRIPTION:Title: Topologically protected vortex knots and links\nby Toni Annala
(University of British Columbia) as part of Bilkent Topology Seminar\n\n\n
Abstract\nThe physical properties of condensed-matter systems can often be
approximated by a "mean field" which\, outside a small singular locus of
the system (defects)\, takes values in a topological space M called the or
der parameter space. A topological vortex is a codimension two defect\, ab
out which the order parameter field winds in a way that corresponds to a n
on-contractible loop in M. If the fundamental group of the order parameter
space is non-Abelian\, then these vortices exhibit a remarkable behavior:
not all pairs of topological vortices are free to pass through each other
.\n\nIt is then a natural to wonder if such vortices could be employed in
tying robust linked structures in physical fields. As a minimum\, such a s
tructure should not untie via strand crossings and local reconnections\, w
hich are the usual means of decay for knotted and linked vortex loops. In
this talk\, we will present several examples of such structures. Our appro
ach is based on the fact that if the second homotopy group of M is trivial
\, then the order parameter field admits a combinatorial description\, whi
ch\, depending on the fundamental group of M\, can be expressed graphicall
y. Hence\, finding topologically stable tangled structures reduces to cons
tructing nontrivial invariants for "colored" links\, which remain unchange
d in strand crossings and local reconnections.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Oliver (Université PARIS 13)
DTSTART:20220404T103000Z
DTEND:20220404T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/42
DESCRIPTION:Title: A Krull-Remak-Schmidt theorem for fusion systems\nby Bob Oliver
(Université PARIS 13) as part of Bilkent Topology Seminar\n\nLecture hel
d in SB-Z11.\n\nAbstract\nThe Krull-Remak-Schmidt theorem\, when restricte
d to finite groups\, implies \nthat every finite group factorizes as a pro
duct of indecomposable subgroups \nwhich are unique up to isomorphism. But
the theorem actually says much \nmore. For example\, as a special case\,
it implies that this factorization is \nunique (not only up to isomorphism
) whenever the group is perfect or \nhas trivial center. This is important
\, for example\, when describing the \nautomorphisms of the group in terms
of the automorphisms of its \nindecomposable factors.\n\nA similar factor
ization theorem is true for fusion systems over finite \n$p$-groups (in fa
ct\, for fusion systems over discrete $p$-toral groups). In \nthis talk\,
I plan to begin by discussing the original theorem for groups \nand sketch
ing its proof\, and then\, after a brief introduction to fusion \nsystems\
, describe how these ideas can be carried over \nto prove the correspondin
g result in that setting.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Torres (Trinity Western University)
DTSTART:20220418T140000Z
DTEND:20220418T150000Z
DTSTAMP:20260424T221812Z
UID:BilTop/43
DESCRIPTION:Title: Sequential Motion Planning assisted by Group Actions\nby Enriqu
e Torres (Trinity Western University) as part of Bilkent Topology Seminar\
n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk I will revisit the co
ncept of effectual and effective topological complexity (TC) in the contex
t of sequential motion planning. These invariants provide a natural contex
t to incorporate group actions into the study of the motion planning probl
em. Related to these invariants\, I will talk about a third version of TC
that incorporates the group action into its planners\, which we call orbit
al topological complexity. I will discuss how they relate to each other an
d to the TC of the quotient space. I will also present some calculations f
or actions of the group of order two on orientable surfaces and spheres.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Henke (TU Dresden)
DTSTART:20220425T120000Z
DTEND:20220425T130000Z
DTSTAMP:20260424T221812Z
UID:BilTop/44
DESCRIPTION:Title: Fusion systems\, linking systems and punctured groups\nby Ellen
Henke (TU Dresden) as part of Bilkent Topology Seminar\n\nLecture held in
SB-Z11.\n\nAbstract\nSaturated fusion systems and associated linking syst
ems are categories modelling the $p$-local structure of finite groups. In
particular\, linking systems contain the algebraic information that is nee
ded to study $p$-completed classifying spaces of fusion systems similarly
to $p$-completed classifying spaces of finite groups. If $G$ is a finite
group and $S$ is a Sylow $p$-subgroup of $G$\, then we can construct a sat
urated fusion system $\\F_S(G)$ as follows: The objects are all subgroups
of $S$\, and the morphisms between two objects are the injective group hom
omorphisms induced by conjugation with elements of $G$. Saturated fusion s
ystems which do not arise in this way are called exotic.\n\n\n\nThe concep
t of a linking system was generalized by Oliver and Ventura to transporter
systems. Andrew Chermak introduced moreover group-like structures\, calle
d localities\, which correspond in a certain way to transporter systems. I
will give an introduction to the subject and outline how the theory of lo
calities can be used to prove new theorems on fusion systems. Moreover\, I
will report on a project with Assaf Libman and Justin Lynd\, where we stu
dy "punctured groups''. Here a transporter system (or a locality) associat
ed to fusion system $\\F$ over $S$ is called a punctured group if the obje
ct set is the collection of all non-identity subgroups. It should be noted
in this context that a fusion system $\\F$ over a $p$-group $S$ can be re
alized as a category $\\F_S(G)$ as above if and only if there is a transpo
rter system whose object set is the full collection of subgroups of $S$. I
n particular\, to every group fusion system one can associate a punctured
group. In the project with Libman and Lynd\, we determine for many of the
known exotic fusion systems whether an associated punctured group exists.\
n
LOCATION:https://stable.researchseminars.org/talk/BilTop/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Facundo Mémoli (Ohio State University)
DTSTART:20220411T120000Z
DTEND:20220411T130000Z
DTSTAMP:20260424T221812Z
UID:BilTop/45
DESCRIPTION:Title: The Gromov-Hausdorff distance between spheres\nby Facundo Mémo
li (Ohio State University) as part of Bilkent Topology Seminar\n\nLecture
held in SB-Z11.\n\nAbstract\nThe Gromov-Hausdorff distance is a fundamenta
l tool in Riemanian geometry\, and also in applied geometry and topology.
Whereas it is often easy to estimate the value of the distance between two
given metric spaces\, its precise value is rarely easy to determine. Som
e of these estimates follow from considerations related to the notion of '
persistent homology' and Gromov's filling radius. However\, these turn out
to be non-sharp.\n\n\nIn this talk I will describe results that we have o
btained which permit calculating the precise value to the Gromov-Hausdorff
between certain pairs of spheres (endowed with their geodesic distance).
These results involve lower bounds\, which arise from certain versions of
the Borsuk-Ulam theorem which are applicable to discontinuous maps\, and f
rom the construction of specialized ``correspondences" between spheres wh
ich yield matching upper bounds in some cases.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Blanc (Haifa University)
DTSTART:20230206T103000Z
DTEND:20230206T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/46
DESCRIPTION:Title: An introduction to infinity categories\nby David Blanc (Haifa U
niversity) as part of Bilkent Topology Seminar\n\n\nAbstract\nIn studying
the homotopy theory of topological spaces it soon becomes apparent that th
e homotopy category itself is not sufficient\, since many homotopy invaria
nts cannot be described or calculated in that category.\n\nSince there are
other settings\, such as the chain complexes of homological algebra\, in
which this holds\, Quillen proposed an axiomatization of such situations i
n terms of model categories. However\, these turn out\n\nto be too restric
tive for dealing with certain questions\, and in particular with homotopy
commutative diagrams and the invariants (such as Toda brackets) which they
encode. Dwyer and Kan suggested an\n\nalternative simplicial approach\, w
hich later devolved into several independent models for what we now call i
nfinity categories\, in terms of simplicially enriched categories\, simpli
cial spaces\, quasi-categories\, and others.\n\nIn the talk we will provid
e examples of questions best addressed in this setting\, and briefly descr
ibe the form they take in the different models\, as time permits.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230213T103000Z
DTEND:20230213T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/47
DESCRIPTION:Title: Simplicial sets\nby Aziz Kharoof (Bilkent University) as part o
f Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThis ta
lk aims to introduce and recall basic notions on simplicial sets. Apart fr
om basic definitions\, we would like to discuss the following notions: wea
k equivalences\, Kan complexes\, Kan fibrations\, and geometric realizatio
n. Also\, the adjunction between singular simplicial set and geometric rea
lization should be covered.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230220T103000Z
DTEND:20230220T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/48
DESCRIPTION:Title: Quasicategories\nby Aziz Kharoof (Bilkent University) as part o
f Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this
talk we will introduce the first model of infinity categories\, namely qu
asicategories. We will discuss the construction of a nerve of a category a
nd thus embedding of the category of (small) categories in sSet. We will a
lso see how a topological space gives rise to a quasicategory – i.e.\, v
ia the fundamental infinity-groupoid construction.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230227T103000Z
DTEND:20230227T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/49
DESCRIPTION:Title: Basic constructions in quasicategories\nby Igor Sikora (Bilkent
University) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11
.\n\nAbstract\nThe goal of this talk is the discussion of the basic notion
s and constructions in the theory of infinity categories. We want to discu
ss the following constructions: the product of quasicategries\, homotopy c
ategory of a quasicategory\, join\, slices and\, most importantly\, colimi
ts and limits.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mustafa Akkaya (Bilkent University)
DTSTART:20230313T103000Z
DTEND:20230313T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/50
DESCRIPTION:Title: Model categories I - basic definitions\nby Mustafa Akkaya (Bilk
ent University) as part of Bilkent Topology Seminar\n\nLecture held in SB-
Z11.\n\nAbstract\nThe goal of this talk is to provide basic definitions of
the theory model categories. We would like to introduce the definition of
a model category and its homotopy category. In particular\, this will req
uire a discussion of fibrations\, cofibrations and weak equivalences\, fib
rant and cofibrant objects\, cylinder and path objects. Then we will proce
ed to the notion of left and right homotopy and define the homotopy catego
ry of a model category. The whole theory will be shown using two examples:
Quillen model structure on topological spaces and Quillen model structure
on simplicial sets.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230320T103000Z
DTEND:20230320T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/51
DESCRIPTION:Title: Model Categories II - Derived functors and Quillen adjunctions\
nby Igor Sikora (Bilkent University) as part of Bilkent Topology Seminar\n
\nLecture held in SB-Z11.\n\nAbstract\nHaving the notion of a homotopy cat
egory\, we will define the notion of a derived functor. Further on\, we wi
ll proceed to the idea of comparing model structures and their homotopy ca
tegories by Quillen functors. Therefore we will cover Quillen functors\, Q
uillen adjunctions and Quillen equivalences. We will also prove that Quill
en model structures on simplicial sets and topological spaces are Quillen
equivalent. The talk will finish with a model structure on simplicial sets
which is relevant for the theory of quasicategories\, i.e.\, the Joyal mo
del structure.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230327T103000Z
DTEND:20230327T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/52
DESCRIPTION:Title: Simplicial Categories I\nby Igor Sikora (Bilkent University) as
part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\n
In this talk\, we will discuss the second model of infinity categories: ca
tegories enriched over simplicial sets. We will start with a short overvie
w of enriched categories and follow to the simplicial categories. We will
also introduce simplicial functors and the homotopy category of a simplici
al category. Then we will proceed with the Bergner model structure and ske
tch the proof of the fact that it is indeed a model structure.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230403T103000Z
DTEND:20230403T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/53
DESCRIPTION:Title: Simplicial categories II - Dwyer-Kan localizations\nby Aziz Kha
roof (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture h
eld in SB-Z11.\n\nAbstract\nThe goal of this talk will be to understand th
e idea of localization of a category with respect to the class of maps and
see how Dwyer-Kan localization is an example of such. Therefore we will s
tart with the notion of a localization of a category. Then we will proceed
to several approaches to the Dwyer-Kan localization - as a derived functo
r with specific resolution and the hammock version\, that gives a construc
tive description of the homotopy category. We will discuss the relation of
DK localization of a simplicial model category and of its homotopy catego
ry.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özgün Ünlü (Bilkent University)
DTSTART:20230410T103000Z
DTEND:20230410T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/54
DESCRIPTION:Title: Segal spaces I\nby Özgün Ünlü (Bilkent University) as part
of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThis t
alk will prepare a background for the third model of infinity categories:
complete Segal spaces. Therefore the following topics should be discussed:
bisimplicial sets\, model structures on functor categories\, Reedy model
structure as an example of the injective model structure and Rezk nerve of
a category.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Oliver (Université PARIS 13)
DTSTART:20230417T103000Z
DTEND:20230417T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/55
DESCRIPTION:by Bob Oliver (Université PARIS 13) as part of Bilkent Topolo
gy Seminar\n\nLecture held in SB-Z11.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230424T103000Z
DTEND:20230424T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/56
DESCRIPTION:Title: Segal spaces II\nby Igor Sikora (Bilkent University) as part of
Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this
talk\, we will continue introducing the third model of infinity categories
: complete Segal spaces. The following notions will be covered: Segal spac
es\, homotopy category of Segal spaces\, completeness of Segal spaces and
CSS model structure.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20230502T103000Z
DTEND:20230502T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/57
DESCRIPTION:Title: Homotopy Coherent Nerve\nby Redi Haderi (Bilkent University) as
part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\n
In this talk\, we aim to understand the equivalences between two different
models of infinity-categories: Simplicial categories and quasi-categories
. We will define the homotopy coherent nerve as a functor from simplicial
categories to simplicial sets\, construct its left adjoint\, and we will s
how how this gives us a Quillen equivalence between the described model ca
tegories.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Bergner (University of Virginia)
DTSTART:20230516T130000Z
DTEND:20230516T140000Z
DTSTAMP:20260424T221812Z
UID:BilTop/58
DESCRIPTION:Title: Complete Segal spaces and generalizations to higher $(\\infty\,n)$-
categories\nby Julie Bergner (University of Virginia) as part of Bilke
nt Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nComplete Segal
spaces provide one of the nicest models for $(\\infty\,1)$-categories fro
m the perspective of homotopy theory\, since the model structure can be ob
tained as a localization of the Reedy model structure on simplicial spaces
. In this talk\, we'll recall complete Segal spaces and their model struc
ture\, and then compare them with other models. We will then look at some
of the ways these comparisons can be generalized higher $(\\infty\,n)$-ca
tegories.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Antonio Torres Castillo (CIMAT)
DTSTART:20230522T153000Z
DTEND:20230522T170000Z
DTSTAMP:20260424T221812Z
UID:BilTop/59
DESCRIPTION:Title: Stable homotopy type of p-local finite groups via biset functors\nby Victor Antonio Torres Castillo (CIMAT) as part of Bilkent Topology S
eminar\n\nLecture held in SB-Z11.\n\nAbstract\nThe Martino-Priddy conjectu
re (now a theorem) says that the p-fusion of G can be recovered (up to iso
morphism) from the unstable homotopy type of BG^p. By making strong use of
the Segal conjecture\, the same authors approached a stable analogous of
that result. In this talk\, we will explore some consequences of the (so-c
alled) stable Martino-Priddy conjecture and their generalizations for p-lo
cal finite groups.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (The University of Virginia)
DTSTART:20230523T133000Z
DTEND:20230523T150000Z
DTSTAMP:20260424T221812Z
UID:BilTop/60
DESCRIPTION:Title: A story about spans\nby Walker Stern (The University of Virgini
a) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstr
act\nSpans in a category C arise in a variety of disparate contexts\, from
the study partially defined functions between sets to Lagrangian correspo
ndences in symplectic geometry. In this talk\, I will give an overview of
some of these connections and tell a story which leads from algebras in ca
tegories of spans to operads. Along the way\, I will discuss past and ongo
ing work (part of the latter joint with Ivan Contreras and Rajan Mehta) an
alyzing and classifying various algebraic structures in spans.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haihan Wu (The University of California\, Davis)
DTSTART:20230524T153000Z
DTEND:20230524T170000Z
DTSTAMP:20260424T221812Z
UID:BilTop/61
DESCRIPTION:Title: Webs and Clasps\nby Haihan Wu (The University of California\, D
avis) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAb
stract\nThe discovery of the Jones polynomial triggered mathematical\ndeve
lopments in areas including knot theory and quantum algebra. One way\nto d
efine the Jones polynomial is by using the braiding in the Temperley-Lieb\
ncategory\, which can be defined with planar matching. We can use diagrams
\nand graphical calculations in the Temperley-Lieb category to study the r
ep-\nresentation theory of quantum sl2. The irreducible representations ca
n be\n“visualized” as the Jones-Wenzl projectors\, which can be used t
o compute\ncolored Jones polynomial and quantum sl2 3-manifold invariant.\
n\nThe sl2 case is generalized to other simple Lie algebras by introducing
triva-\nlent vertices\, and the generalized graphical categories are call
ed spiders or web\ncategories. Clasps are defined as analogues of the Jone
s-Wenzl projectors\, and\nwe can use clasps to compute colored quantum lin
k invariants\, quantum 3-\nmanifold invariants\, 3-j symbols\, and 6-j sym
bols of different quantum groups.\n\nIn this talk\, I will review the back
ground material\, and talk about re-\ncent developments on definition of w
eb categories and clasp expansions for\ndifferent Lie types.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20230925T103000Z
DTEND:20230925T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/62
DESCRIPTION:Title: Homotopical characterization of strong contextuality (part I)\n
by Aziz Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n
\nLecture held in SB-Z11.\n\nAbstract\nSimplicial distributions introduced
in the paper “Simplicial quantum contextuality” provide a topological
approach to the study of contextuality for collections of probability dis
tributions. The space of measurements and the space of outcomes are repres
ented by simplicial sets\, so one can ask what is the role of the homotopy
theory of simplicial sets here. In this talk\, we will give a homotopical
characterization of strongly contextual simplicial distributions with bin
ary outcomes\, specifically those defined on the cone of a 1-dimensional s
pace. To prove this\, we introduce the corresponding category for simplici
al distribution on the cone of a 1-dimensional space and give the characte
rization of strong contextuality in terms of this category.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20231002T103000Z
DTEND:20231002T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/63
DESCRIPTION:Title: Homotopical characterization of strong contextuality (part II)\
nby Aziz Kharoof (Bilkent University) as part of Bilkent Topology Seminar\
n\nLecture held in SB-Z11.\n\nAbstract\nSimplicial distributions introduce
d in the paper “Simplicial quantum contextuality” provide a topologica
l approach to the study of contextuality for collections of probability di
stributions. The space of measurements and the space of outcomes are repre
sented by simplicial sets\, so one can ask what is the role of the homotop
y theory of simplicial sets here. In this talk\, we will give a homotopica
l characterization of strongly contextual simplicial distributions with bi
nary outcomes\, specifically those defined on the cone of a 1-dimensional
space. To prove this\, we introduce the corresponding category for simplic
ial distribution on the cone of a 1-dimensional space and give the charact
erization of strong contextuality in terms of this category.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20231009T103000Z
DTEND:20231009T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/64
DESCRIPTION:Title: Colimits of categories\, zig-zags and necklaces\nby Redi Haderi
(Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held
in SB-Z11.\n\nAbstract\nColimits of simplicial categories are generally co
nsidered hard to understand in explicit terms. Important simplicial catego
ries\, such as those freely generated by simplicial sets\, arise as such c
olimits. In fact\, the free simplicial category - coherent nerve adjunctio
n has been demonstrated by Lurie to be a Quillen equivalence.\nWe discuss
how the problem of computing colimits of simplicial categories reduces to
computing colimits of categories. Then\, we present a theorem which descri
bes the latter in explicit terms (to the best of our knowledge\, not in th
e literature). As an application\, we provide a computational proof of the
Necklace Theorem of Dugger and Spivak.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora
DTSTART:20231023T103000Z
DTEND:20231023T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/65
DESCRIPTION:Title: Equivariant contextuality\nby Igor Sikora as part of Bilkent To
pology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nSimplicial quantum
contextuality\, introduced by Okay\, Kharoof and Ipek\, is a framework for
using topological methods based on simplicial sets to study quantum conte
xtuality. It subsumes earlier approaches - topological (Okay\, Roberts\, B
artlett\, Raussendorf) and sheaf-theoretic (Abramsky\, Brandenburger).\n\n
In this talk we will discuss how group action can be composed into this fr
amework. To this end\, we will use such tools as Borel construction and pa
rtial groups in the sense of Broto-Gonzalez. We will start with the notion
s of equivariant simplicial distributions and equivariant contextuality an
d connect them with the Borel construction. Then we will proceed with the
cohomological aspects\, which are based on the extensions of partial group
s and cofibre sequences of simplicial sets.\n\nThe talk is based on a join
t work with Cihan Okay\, to appear on arxiv soon.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Cantarero
DTSTART:20231030T140000Z
DTEND:20231030T150000Z
DTSTAMP:20260424T221812Z
UID:BilTop/66
DESCRIPTION:Title: Configuration spaces of commuting elements\nby Jose Cantarero a
s part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\
nThe rational cohomology of the configuration space of commuting\nelements
in a compact Lie group is determined by the action of the Weyl group on t
he configuration space of its maximal torus. This can be used to determine
(co)homological stability phenomena and other unstable computations. In t
his talk I will begin with some motivation for the study of these spaces a
nd the case of SU(2)\, where the homotopy type can be completely determine
d. Then I will describe the stability results mentioned previously and oth
er interesting cohomology computations. This is joint work with Ángel R.
Jiménez.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Koray Karabina
DTSTART:20231106T103000Z
DTEND:20231106T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/67
DESCRIPTION:Title: Secure Boundary Matrix Reduction Algorithm Using Homomorphic Encryp
tion\nby Koray Karabina as part of Bilkent Topology Seminar\n\nLecture
held in SB-Z11.\n\nAbstract\nTopological Data Analysis (TDA) offers a sui
te of computational tools that provide quantified shape features in high-d
imensional data\, which can be utilized by modern statistical and predicti
ve machine learning models. In particular\, persistent homology (PH) takes
in data and derives compact representations of latent topological structu
res\, known as persistence diagrams. PH has been widely adopted for model
development on sensitive data\, motivating the computation of PH on encryp
ted data. In this presentation\, I will provide brief introductions to TDA
and secure computing and then demonstrate how to modify the boundary matr
ix reduction algorithm to compute PH on encrypted data using homomorphic e
ncryption.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Torres Castillo
DTSTART:20231113T103000Z
DTEND:20231113T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/68
DESCRIPTION:Title: Partial group cohomology\nby Victor Torres Castillo as part of
Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nPartial g
roups were introduced by Chermak as a tool to approach the issue of the ex
istence and uniqueness of a centric linking system for a saturated fusion
system. Roughly speaking\, a partial group is a set with a partially defin
ed product (you can still multiply certain strings of elements together\,
but not always).\nIn this talk\, we will discuss the main similarities and
differences between the categories of partial groups and (actual) groups.
Then\, we will introduce the cohomology of a partial group inspired by th
e Gabriel-Zisman cohomology\, as defined by Galvez-Neumann-Tonks.\nThe tal
k is based on a joint work in progress with Cihan Okay and Igor Sikora.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Kirtisoglu
DTSTART:20231120T103000Z
DTEND:20231120T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/69
DESCRIPTION:Title: Thomason's Homotopy Colimit Theorem\nby Mehmet Kirtisoglu as pa
rt of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn
this talk\, we will discuss the proof of Thomason's homotopy colimit theor
em. The theorem states that given a functor from a small category to the c
ategory of small categories\, the homotopy colimit construction on the ner
ves of the categories in the diagram is naturally homotopy equivalent to
the nerve space of the Grothendieck Construction.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern
DTSTART:20231127T103000Z
DTEND:20231127T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/70
DESCRIPTION:Title: $(\\infty\,2)$-categories and lax colimits\nby Walker Stern as
part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nM
any higher-categorical structures\, most notably $(\\infty\,1)$-categories
themselves\, form $(\\infty\,2)$-categories. It is thus highly desirable
to characterize such structures in terms of $(\\infty\,2)$-categorical uni
versal properties. One recent framework allowing us to understand such $(\
\infty\,2)$-categorical universal properties is the theory of (co)limits i
n $(\\infty\,2)$-categories. In this talk\, I will explain the developing
theory of (partially) lax colimits in $(\\infty\,2)$-categories\, and disc
uss how it recovers a number of previous notions in the literature. I will
then explain how one can generalize from the $(\\infty\,1)$-categorical s
etting to obtain a cofinality criterion for $(\\infty\,2)$-functors. This
work was joint with Fernando Abellán.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ivan Piterman
DTSTART:20231204T103000Z
DTEND:20231204T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/71
DESCRIPTION:Title: Advances on Quillen's conjecture\nby Kevin Ivan Piterman as par
t of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nThe
study of the p-subgroup complexes began motivated by group cohomology and
equivariant cohomology of topological spaces "modulo the prime p". For exa
mple\, Kenneth Brown proved that the reduced Euler characteristic of this
complex is divisible by the size of a Sylow p-subgroup\, giving rise to a
sort of "Homological Sylow theorem". Later\, he showed that the mod-p equi
variant cohomology of the p-subgroup complex of a finite group coincides w
ith the mod-p cohomology of the group. Deeper relations with finite group
theory\, representation theory\, and finite geometries were also explored.
For instance\, uniqueness of certain simple groups\, finite geometries fo
r sporadic groups\, Lefschetz modules\, and\, more recently\, endotrivial
modules.\n\nIn 1978\, Daniel Quillen conjectured that the poset of non-tri
vial p-subgroups of a finite group G is contractible if and only if G has
non-trivial p-core. Quillen established the conjecture for solvable groups
and some families of groups of Lie type. The major step towards the resol
ution of the conjecture was done by Michael Aschbacher and Stephen D. Smit
h at the beginning of the nineties. They roughly proved that if p>5 and G
is a group of minimal order failing the conjecture\, then G contains a sim
ple component PSU(n\,q^2) failing a certain homological condition denoted
by (QD) (namely\, the top-degree homology group of its p-subgroup poset do
es not vanish).\n\nIn this talk\, I will present recent advances in the co
njecture\, with a particular focus on the prime p=2\, which was not covere
d by the methods developed by Aschbacher-Smith. In particular\, we show th
at the study of the conjecture for the prime p=2 basically reduces to stud
ying (QD) on the poset of p-subgroups of certain families of classical gro
ups. Part of this work is in collaboration with S.D. Smith\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer
DTSTART:20231211T103000Z
DTEND:20231211T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/72
DESCRIPTION:Title: Filling Radius and Persistent Homology\nby Baris Coskunuzer as
part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nI
n this talk\, we discuss interesting relations between notions from applie
d topology and metric geometry in point cloud setting. First\, we introduc
e several notions in both fields to measure the size of a manifold. Then\,
for a point cloud X in R^n\, we relate the life spans of the topological
features to their extrinsic and Gromov’s filling radius in R^n\, and by
using this relation\, we give bounds for them with Urysohn width. Next\, w
e discuss an interesting relationship between the life spans of the topolo
gical features in PD_k(X) in R^n and l^\\infty principal components (PCA_\
\infty) of the point cloud X.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer
DTSTART:20231211T133000Z
DTEND:20231211T143000Z
DTSTAMP:20260424T221812Z
UID:BilTop/73
DESCRIPTION:Title: Topological Machine Learning and Applications in Drug Discovery and
Cancer Detection\nby Baris Coskunuzer as part of Bilkent Topology Sem
inar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, we'll introduc
e fundamental techniques in topological machine learning and showcase thei
r application in two specific contexts. The first application is on comput
er-aided drug discovery\, utilizing Multiparameter Persistence for graph r
epresentation learning. Our second application revolves around cancer dete
ction from histopathological images via cubical persistence. We apply our
methodologies across five distinct cancer types\, demonstrating superior p
erformance compared to state-of-the-art deep learning methods. The talk is
accessible to graduate students in math\, science\, and engineering\, ass
uming no prior background in topology or machine learning.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Imma Gálvez Carrillo
DTSTART:20231218T103000Z
DTEND:20231218T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/74
DESCRIPTION:Title: Cohomology of categories after Baues-Wirsching\nby Imma Gálvez
Carrillo as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n
\nAbstract\nIn this talk\, I will revise some aspects and generalizations
of the cohomology\nof small categories introduced by Baues and Wirsching i
n 1985 developed in more\nrecent work with Neumann and Tonks\, such as Tho
mason cohomology and\n Gabriel-Zisman cohomology for simplicial sets.\nAls
o\, I will report about work in progress with Neumann\, Paoli and\nTonks a
bout the generalization of the above to the framework of 2-categories.\nTh
is has applications for instance to higher Segal spaces.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20240205T103000Z
DTEND:20240205T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/75
DESCRIPTION:Title: TDA I: An Introduction to Topological Data Analysis\nby Ergun Y
alcin (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SB-Z11.\n\nAbstract\nTopological Data Analysis is an emerging area
of mathematics where topological\nmethods are used to analyze data. One o
f the most important tools for TDA is Persistent\nHomology. The input of t
his process is a finite metric space (a data cloud) and the output\nis a b
arcode or a persistent diagram. Given a finite metric space\, using closed
balls\nof changing radius\, we build a filtered simplicial complex. The h
omology modules of these\nfiltered simplicial complexes are called persist
ent homology modules and they are\nexpressed using barcodes or persistent
diagrams. What makes this method very useful\nis that the persistent homol
ogy calculations can be done using a simple matrix algorithm\,\ncalled the
reduction algorithm. I will introduce basic ideas behind persistent homol
ogy\nand show how the reduction algorithm works. Most of the talk should b
e accessible to\nan undergraduate student who has taken a linear algebra c
ourse.\n\nPart I of a sequel on Topological Data Analysis (TDA).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240212T103000Z
DTEND:20240212T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/76
DESCRIPTION:Title: HC I: Quasi-categories and simplicially enriched categories\nby
Walker Stern (Bilkent University) as part of Bilkent Topology Seminar\n\n
Lecture held in SB-Z11.\n\nAbstract\nIn this talk\, we define quasi-catego
ries as simplicial sets satisfying a lifting condition related to both cat
egories and Kan complexes. We describe an adjunction that relates quasi-ca
tegories and simplicially enriched categories and explain\nhow it allows u
s to define some first categorical notions in quasi-categories.\n\nPart I
of a sequel on Higher Categories (HC).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Praderio (Lancaster University)
DTSTART:20240219T103000Z
DTEND:20240219T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/77
DESCRIPTION:Title: Sharpness for the Benson-Solomon fusion systems\nby Marco Prade
rio (Lancaster University) as part of Bilkent Topology Seminar\n\nLecture
held in SB-Z11.\n\nAbstract\nSince their appearance fusion systems have re
ceived much interest in both algebra and topology and in 2011 Asbacher\, K
essar and Oliver published a list of problems involving fusion systems man
y of which remain nowadays open. One of such problems was rephrased in a m
ore general way by Díaz and Park in 2013 and has since been known as the
sharpness for fusion systems conjecture. This conjecture has seen a lot of
activity in recent years. During this talk we will briefly go over the co
ncepts of fusion system and Mackey functor\, use those in order to properl
y state the sharpness conjecture\, mention the results we know involving t
his conjecture and finally sketch the proof that the Benson-Solomon fusion
systems (the only known family of exotic fusion systems over 2 groups) sa
tisfy this conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240226T103000Z
DTEND:20240226T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/78
DESCRIPTION:Title: HC II: First constructions\nby Walker Stern (Bilkent University
) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstra
ct\nWe explain how slice quasi-categories are defined\, and how they provi
de a new notion of mapping spaces in a quasi-category. Using this new noti
on\, we give an alternate\ncharacterization of equivalences of quasi-categ
ories\, and define initial and terminal objects in a quasi-\ncategory.\n\n
Part II of a sequel on Higher Categories (HC).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uzay Cetin (Bilkent University)
DTSTART:20240304T103000Z
DTEND:20240304T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/79
DESCRIPTION:Title: TDA II: Matrix Reduction Algorithm and Morozov's Worst Case Example
\nby Uzay Cetin (Bilkent University) as part of Bilkent Topology Semin
ar\n\nLecture held in SB-Z11.\n\nAbstract\nMatrix reduction algorithm on a
simplicial complex is a fairly new wave in persistent homology due to its
implementations on programs like Ripser and many algorithms that have bee
n built upon that. Persistent algorithm dates back to 2002 with a pairing
algorithm and its runtime has been shown to be O(N^3). Morozov in his 2005
article gives an explicit example of the existence of this case. In my ta
lk\, I will talk about the matrix reduction and how it is done\, and expla
in why the example runs at O(N^3) by combining the logic behind pairing an
d matrix algorithms. After that\, I will also mention an alternative examp
le and in which ways it improves the original example.\n\nPart II of a seq
uence on Topological Data Analysis (TDA).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kadri İlker Berktav (Bilkent University)
DTSTART:20240311T103000Z
DTEND:20240311T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/80
DESCRIPTION:Title: Homotopy theory of stacks and higher structures\nby Kadri İlke
r Berktav (Bilkent University) as part of Bilkent Topology Seminar\n\nLect
ure held in SB-Z11.\n\nAbstract\nIn this talk\, we outline Hollander's hom
otopy theory of stacks and give some examples. We also briefly discuss mor
e general stacks and certain higher structures on them in the context of d
erived algebraic/symplectic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240318T103000Z
DTEND:20240318T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/81
DESCRIPTION:Title: HC III: $\\text{Cat}_\\infty$ and Grothendieck\nby Walker Stern
(Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held
in SB-Z11.\n\nAbstract\nWe describe how one may define the (large) $\\inft
y$-category of small\n$\\infty$-categories using simplicial sets and simpl
icially enriched categories. We then sketch the idea of the Grothendieck-L
urie construction for quasi-categories\, and discuss applications.\n\nTalk
III in the sequence of Higher Categories (HC).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240325T103000Z
DTEND:20240325T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/82
DESCRIPTION:Title: HC IV: Limits and colimits\nby Walker Stern (Bilkent University
) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstra
ct\nWe define limits and colimits in a quasi-category\, and describe how\n
they generalize both 1-categorical limits\, and homotopy limits. We survey
some theorems about the computation of limits and colimits — in particu
lar\, cofinality.\n\n\nPart IV of a sequnce on Higher Categories (HC).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozgun Unlu (Bilkent University)
DTSTART:20240401T103000Z
DTEND:20240401T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/83
DESCRIPTION:Title: Zigzag Persistence in Topological Data Analysis\nby Ozgun Unlu
(Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held i
n SB-Z11.\n\nAbstract\nZigzag Persistence is a pivotal technique within th
e Topological Data Analysis (TDA) domain. This talk delves into the mathem
atical underpinnings and algorithmic implementations of Zigzag Persistence
\, elucidating its efficacy in capturing the dynamic evolution of topologi
cal structures across varying resolutions. Through a rigorous examination
of Zigzag Persistence diagrams and their interpretation\, we discuss its p
otential to find subtle patterns and extract information from high-dimensi
onal data spaces.\n\nPart III of a sequence on Topological Data Analysis (
TDA).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Hackney (University of Louisiana at Lafayette)
DTSTART:20240422T130000Z
DTEND:20240422T140000Z
DTSTAMP:20260424T221812Z
UID:BilTop/84
DESCRIPTION:Title: Partial groups and symmetric simplicial sets\nby Philip Hackney
(University of Louisiana at Lafayette) as part of Bilkent Topology Semina
r\n\nLecture held in SA 141.\n\nAbstract\nPartial groups are a generalizat
ion of groups which allow for the possibility that some n-fold products of
elements may be undefined. They were introduced by Chermak to serve in th
e study of the p-local structure of a finite group. These partial groups m
ay be viewed as certain simplicial sets\, or better yet\, as certain symme
tric simplicial sets. I'll explain this viewpoint\, as well as some implic
ations. I will also touch on the question about which partial groups are h
igher Segal spaces. This is joint work with Justin Lynd.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Oliver (Université Sorbonne Paris Nord)
DTSTART:20240506T103000Z
DTEND:20240506T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/85
DESCRIPTION:by Bob Oliver (Université Sorbonne Paris Nord) as part of Bil
kent Topology Seminar\n\nLecture held in SB-Z11.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20240520T103000Z
DTEND:20240520T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/86
DESCRIPTION:Title: What is an infinity operad? (part I)\nby Redi Haderi (Bilkent U
niversity) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\
n\nAbstract\nWe propose a combinatorial model for non-symmetric infinity o
perads. Our approach is simplicial\, except that the simplicial objects we
study take values in a category of sets in which morphisms assign lists o
f elements in the codomain to an element in the domain.\nWe briefly discus
s ordinary operads and their algebras in order to motivate our constructio
ns. This is joint work with Özgün Ünlü.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Castillo (Bilkent University)
DTSTART:20240415T103000Z
DTEND:20240415T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/87
DESCRIPTION:Title: Quantum nonlocal games and the d-torsion commutative space\nby
Victor Castillo (Bilkent University) as part of Bilkent Topology Seminar\n
\nLecture held in SB-Z11.\n\nAbstract\nNonlocal games have played a promin
ent role in quantum information theory by demonstrating the power of non-l
ocality. In particular\, the 'magic' examples due to Mermin and Peres belo
ng to the class of linear system games. The Mermin-Peres games have no cla
ssical solutions\, but they admit operator solutions.\n\nIn this talk\, we
translate the problem of finding operator solutions into a problem of ext
ensions for partial groups (in the sense of Broto-Gonzalez). In particular
\, we define the d-torsion commutative nerve for groups\, whose homotopy s
tructure is crucial to identify a practical criterion (in terms of higher
limits) to test a conjecture due to Chung-Okay-Sikora regarding linear sys
tem games over Z_d\, with d odd.\n\nThis is joint work with Ho Yiu Chung a
nd Cihan Okay.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Bauer (Technical University of Munich)
DTSTART:20240513T103000Z
DTEND:20240513T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/88
DESCRIPTION:Title: Connect the dots: from data through complexes to persistent homolog
y\nby Ulrich Bauer (Technical University of Munich) as part of Bilkent
Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nIn this talk\, I
will survey some recent results on theoretical and computational aspects
of applied topology. I will illustrate various aspects of persistent homol
ogy: its structure\, which serves as a topological descriptor\, its stabil
ity with respect to perturbations of the data\, its computation on a large
scale\, and connections to Morse theory.\n\nThese aspects will be motivat
ed and illustrated by concrete examples and applications\, such as\n\n* r
econstruction of a shape and its homology from a point cloud\,\n\n* faith
ful simplification of contours of a real-valued function\,\n\n* existence
of unstable minimal surfaces\, and\n\n* identification of recurrent muta
tions in the evolution of COVID-19.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20240527T103000Z
DTEND:20240527T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/91
DESCRIPTION:Title: What is an infinity operad? (part 2)\nby Redi Haderi (Bilkent U
niversity) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\
n\nAbstract\nWe will discuss some of the details of the nerve construction
which we presented in the previous talk. Then\, we will explain how the c
ategory of simplicial lists has the structure of a presheaf category. We w
ill also present a homotopy coherent nerve construction which\, among othe
r things\, outputs a quasi-operad for all operads enriched in Kan complexe
s. This is joint work with Özgün Ünlü.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cihan Okay (Bilkent University)
DTSTART:20241028T103000Z
DTEND:20241028T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/92
DESCRIPTION:Title: Introduction to simplicial distributions\nby Cihan Okay (Bilken
t University) as part of Bilkent Topology Seminar\n\nLecture held in SA 14
1.\n\nAbstract\nSimplicial distributions [1] is a new approach to studying
measurement statistics of experiments\, mainly quantum\, from a topologic
al perspective. The topology that comes in is combinatorial in flavor and
is based on the theory of simplicial sets. In this talk\, I will introduce
the basic notions of the theory and explain the origins connecting to ear
lier work on preserves of distributions by Abramsky--Brandenburger.\n\n[1]
Simplicial quantum contextuality\, https://arxiv.org/abs/2204.06648\n\n(T
his talk is part of the reading seminar series on the theory and applicati
ons of simplicial distributions.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20241104T103000Z
DTEND:20241104T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/93
DESCRIPTION:Title: Simplicial distributions\, convex categories\, and contextuality\nby Aziz Kharoof (University of Haifa) as part of Bilkent Topology Semin
ar\n\nLecture held in SA 141.\n\nAbstract\nIn a quantum mechanical experim
ent\, the data describing outcome probabilities consists of a family of pr
obability distributions indexed by subsets of jointly permissible measurem
ents. The simplicial framework introduced in the first talk models this da
ta as a morphism in the Kleisli category associated with the distribution
monad. By studying certain properties of the distribution monad\, we gain
insights into the enriched structure of this Kleisli category. These categ
ories\, referred to as convex categories\, have a one-object version known
as convex monoids. In this talk\, we characterize contextuality as a mono
id-theoretic concept by introducing a weak notion of invertibility for con
vex monoids. Our main result is that a simplicial distribution is nonconte
xtual if and only if it is weakly invertible.\n\n(This talk is part of the
reading seminar series on the theory and applications of simplicial distr
ibutions.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20241112T103000Z
DTEND:20241112T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/94
DESCRIPTION:Title: The monoid of simplicial distributions\nby Aziz Kharoof (Univer
sity of Haifa) as part of Bilkent Topology Seminar\n\nLecture held in SA 1
41.\n\nAbstract\nIn this talk\, we will discuss the monoid structure of si
mplicial distributions (when the outcome space is a simplicial group) and
its applications. We give some important examples of subgroups and submono
ids when the outcome space is the nerve of a finite cyclic group. We then
show the importance of the action of deterministic distributions on the si
mplicial distributions to understand their geometrical structure. Finally\
, we will introduce the Bell inequalities for a simplicial scenario and de
scribe the action of the deterministic distributions on it.\n\n\n(This tal
k is part of the reading seminar series on the theory and applications of
simplicial distributions.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20241118T103000Z
DTEND:20241118T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/95
DESCRIPTION:Title: Simplicial distributions and polyhedral geometry\nby Selman Ipe
k (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held
in SA 141.\n\nAbstract\nSimplicial distributions are collections of proba
bility distributions that satisfy certain compatibility conditions that ca
n be encoded topologically using simplicial sets. For a simplicial scenari
o where the measurement space X and outcome space Y are finitely generated
the space sDist(X\,Y) of allowed simplicial distributions is a convex set
\, in fact\, a convex polytope. By the Minskowski-Weyl theorem of polytope
theory it is well-known that there are two equivalent descriptions of a c
onvex polytope as the intersection of finitely many half-space inequalitie
s (H-representation) or as the convex hull of finitely many extreme points
(V-representation). In this talk we detail how one constructs the H-repre
sentation of sDist(X\,Y) and discuss the conversion to its V-representatio
n\, known as the vertex enumeration problem. Time permitting\, we will als
o discuss the Bell polytope\, which delineates the boundary between contex
tual and noncontextual measurement statistics\, and is a subpolytope of sD
ist(X\,Y).\n\n(This talk is part of the reading seminar series on the theo
ry and applications of simplicial distributions.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (University of Haifa)
DTSTART:20241126T103000Z
DTEND:20241126T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/96
DESCRIPTION:Title: Gluing and extending simplicial distributions\nby Aziz Kharoof
(University of Haifa) as part of Bilkent Topology Seminar\n\nLecture held
in SA 141.\n\nAbstract\nIn the theory of simplicial distributions\, contex
tuality is determined by a natural map. As a result\, any diagram of measu
rement spaces induces a diagram that can be used to compare contextuality.
In this talk\, we will focus on two cases: (1) an Inclusion map between m
easurement spaces and (2) a pushout square of measurement spaces. These tw
o cases lead to the Extending Lemma and the Gluing Lemma\, respectively. T
he proof of the second Lemma is based on the fact that the distribution mo
nad weakly preserves pullbacks: the natural map from the distribution of a
pullback to the pullback of the distributions has a section. We will show
that this section behaves like a composition.\n\n(This talk is part of th
e reading seminar series on the theory and applications of simplicial dist
ributions.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20241202T103000Z
DTEND:20241202T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/97
DESCRIPTION:Title: Topological methods for studying contextuality and Bell inequalitie
s\nby Selman Ipek (Bilkent University) as part of Bilkent Topology Sem
inar\n\nLecture held in SA 141.\n\nAbstract\nGoing back to the seminal wor
k of J.S. Bell [1]\, and later A. Fine [2] and M. Froissart [3]\, it is po
ssible to study the separation between noncontextual and contextual measur
ement statistics using polyhedral geometry. From this geometric point of v
iew a distribution is termed noncontextual if it lies within the convex hu
ll of so-called deterministic distributions\, and contextual otherwise. Th
e facet defining inequalities of this convex set are called Bell inequalit
ies. In this talk we follow [4] and use the framework of simplicial distri
butions to derive Bell inequalities for the well-known N-cycle scenarios a
nd their generalization\, the flower scenarios first introduced in [4]. We
restrict our attention to outcomes in integers mod 2. Our proof technique
s utilize topological notions\, such as gluing and extension\, together wi
th a topological interpretation of Fourier-Motzkin elimination\, a common
technique used in polytope theory.\nReferences:\n[1] J.S. Bell\, On the Ei
nstein Podolsky Rosen Paradox\n[2] A. Fine\, Hidden variables\, joint prob
ability\, and the Bell inequalities\n[3] M. Froissart\, Constructive gener
alization of Bell's inequalities\n[4] Kharoof\, et al. Topological methods
for studying contextuality: N-cycle scenarios and beyond\n\n(This talk is
part of the reading seminar series on the theory and applications of simp
licial distributions.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20241209T103000Z
DTEND:20241209T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/98
DESCRIPTION:Title: Homotopical characterization of strong contextuality\nby Aziz K
haroof (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SA 141.\n\nAbstract\nFor a simplicial scenario\, the space of mea
surements and the space of outcomes are represented by simplicial sets\, s
o one can ask what the role of the homotopy theory of simplicial sets is i
n the theory of simplicial distributions. In this talk\, we will give a ho
motopical characterization of strongly contextual simplicial distributions
with binary outcomes\, specifically those defined in 1-dimensional space.
To prove this\, we introduce the corresponding category for simplicial di
stribution on 1-dimensional space and characterize strong contextuality in
terms of this category.\n\n(This talk is part of the reading seminar seri
es on the theory and applications of simplicial distributions.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20241224T103000Z
DTEND:20241224T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/100
DESCRIPTION:Title: The category of bundle scenarios of simplicial complexes\nby A
ziz Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n\nLe
cture held in SA 141.\n\nAbstract\nIn this talk\, we begin by introducing
the sheaf-theoretic framework for contextuality. We then define the catego
ry of scenarios\, based on this framework. The definition of morphisms bet
ween scenarios allows us to deal with simulation between empirical models.
Next\, we extend this framework to define the category of bundle scenario
s. A bundle scenario is a map between simplicial complexes that satisfies
specific properties\, allowing it to behave analogously to a contextuality
scenario. The transition from scenarios to bundle scenarios is facilitate
d by the nerve complex functor\, which operates as a monad on simplicial c
omplexes. Finally\, we introduce the concept of an empirical model over a
bundle scenario.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav
DTSTART:20250303T103000Z
DTEND:20250303T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/102
DESCRIPTION:Title: Derived geometry I: Basics of infinity-categories\nby Ilker Ka
dri Berktav as part of Bilkent Topology Seminar\n\nLecture held in SA 141.
\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250317T103000Z
DTEND:20250317T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/104
DESCRIPTION:Title: Derived geometry II: Basics of infinity-categories-2\nby Ilker
Kadri Berktav (Bilkent University) as part of Bilkent Topology Seminar\n\
nLecture held in SA 141.\n\nAbstract\nIn this talk\, we will continue disc
ussing infinity-categories\, focusing on the simplicial categorical descri
ption. We will then study the infinity-category of commutative differentia
l graded algebras\, which will lead to the introduction of derived affine
schemes.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beckham Myers (Einstein Institute of Mathematics)
DTSTART:20250324T103000Z
DTEND:20250324T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/105
DESCRIPTION:Title: Categorification and chromatic homotopy theory\nby Beckham Mye
rs (Einstein Institute of Mathematics) as part of Bilkent Topology Seminar
\n\nLecture held in SA 141.\n\nAbstract\nI will explain the idea of catego
rification\, which is the process of replacing notions like "equality" wit
h "equivalence". We will see that this naturally leads us to consider spec
tra\, the central objects of study in stable homotopy theory. We will conc
lude by introducing the chromatic picture of spectra\, and explaining what
categorification has to say in this context. (No previous knowledge of ho
motopy theory will be assumed.)\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20250407T103000Z
DTEND:20250407T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/107
DESCRIPTION:Title: Simplicial methods in the resource theory of contextuality\nby
Aziz Kharoof (Bilkent University) as part of Bilkent Topology Seminar\n\n
Lecture held in SA 141.\n\nAbstract\nWe introduce the concept of a categor
y of scenarios structured over a monad with a gluing operator. Our main ex
amples are the category of simplicial bundle scenarios and the category of
stochastic bundle scenarios. Using a relative variant of the Grothendieck
construction\, we define the simplicial distribution functor\, which exte
nds the functor of empirical models. Finally\, we leverage contextuality t
o characterize the convex maps between simplicial distributions\, which ar
e convex combinations of maps induced by morphisms in the category of simp
licial bundle scenarios.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250414T103000Z
DTEND:20250414T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/108
DESCRIPTION:Title: Derived geometry III: Introduction to higher spaces\nby Ilker
Kadri Berktav (Bilkent University) as part of Bilkent Topology Seminar\n\n
Lecture held in SA 141.\n\nAbstract\nThis talk introduces the infinity-cat
egory of commutative differential graded algebras\, along with key concept
s and constructions that lead to the description of derived schemes and\,
more generally\, derived stacks.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250421T103000Z
DTEND:20250421T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/109
DESCRIPTION:Title: Derived geometry IV: Introduction to derived symplectic geometry\nby Ilker Kadri Berktav (Bilkent University) as part of Bilkent Topolog
y Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, we will c
ontinue our discussion on the formulation of higher spaces\, following she
af-theoretical approaches. We will then present the basics of shifted symp
lectic structures and related results.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kursat Sozer (McMaster University)
DTSTART:20250505T133000Z
DTEND:20250505T143000Z
DTSTAMP:20260424T221812Z
UID:BilTop/111
DESCRIPTION:Title: Survey of 3-Dimensional TQFTs and Quantum Invariants of 3-Manifold
s\nby Kursat Sozer (McMaster University) as part of Bilkent Topology S
eminar\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, I will give
a gentle overview of 3-dimensional topological quantum field theories (TQF
Ts) and the corresponding quantum invariants of closed 3-manifolds. After
briefly recalling essential algebraic notions such as pivotal\, fusion\, a
nd modular categories\, I will describe the two main constructions of 3-di
mensional TQFTs: the surgery approach (Witten–Reshetikhin–Turaev invar
iants) and the state-sum approach (Turaev–Viro–Barrett–Westbury inva
riants). I will then summarize the key comparison result involving the cat
egorical center construction\, illustrating how these two approaches yield
isomorphic TQFTs. If time permits\, I will close by briefly mentioning ex
tensions to homotopy quantum field theories (HQFTs) and highlight some rec
ent developments in this direction.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eren Uyanik (Bilkent University)
DTSTART:20250512T103000Z
DTEND:20250512T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/112
DESCRIPTION:Title: Introduction to Bicategories and Extended Topological Field Theori
es\nby Eren Uyanik (Bilkent University) as part of Bilkent Topology Se
minar\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, I will motiva
te and introduce bicategories and extended Topological Field Theories (eTF
Ts). I will start with recalling the basics of Topological Quantum Field T
heories (TQFTs) and the classification theorem in 2-dimensional case. I wi
ll then give the definition of eTFT as a functor between particular bicate
gories\, generalizing the case of ordinary TQFT. Lastly\, I will informall
y discuss one of the classification theorems for 2-dimensional eTFTs.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safranov (University of Edinburgh)
DTSTART:20250519T103000Z
DTEND:20250519T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/113
DESCRIPTION:Title: Simple homotopy invariance of the loop coproduct\nby Pavel Saf
ranov (University of Edinburgh) as part of Bilkent Topology Seminar\n\nLec
ture held in SA 141.\n\nAbstract\nString topology provides algebraic opera
tions on the homology of a free loop space of a manifold introduced by Cha
s and Sullivan. While the loop product was known to be homotopy-invariant
for a long time\, Sullivan conjectured that the loop coproduct is not homo
topy-invariant. I will explain a recent proof due to Naef and myself (with
related work by Kenigsberg and Porcelli) that the failure of the loop cop
roduct to be homotopy-invariant is given by the trace of the Whitehead tor
sion from simple homotopy theory.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Kadri Berktav (Bilkent University)
DTSTART:20250526T103000Z
DTEND:20250526T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/114
DESCRIPTION:Title: Derived geometry V: Topics in derived symplectic geometry\nby
Ilker Kadri Berktav (Bilkent University) as part of Bilkent Topology Semin
ar\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, we will continue
our discussion on shifted symplectic structures. We will then present sev
eral key results in DSG. If time permits\, we will briefly mention our wor
k in that setting\, focusing on the development of shifted contact structu
res and related results.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jaz Myers (Topos Institute)
DTSTART:20250502T103000Z
DTEND:20250502T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/115
DESCRIPTION:Title: Double categorical right modules as the algebra of coupled dynamic
al systems\nby David Jaz Myers (Topos Institute) as part of Bilkent To
pology Seminar\n\nLecture held in SA 141.\n\nAbstract\nOpen dynamical syst
ems whose dynamics depend on free parameters and which expose some variabl
es of their state may be coupled by setting their parameters as functions
of the exposed variables of other systems. Together with their parallel (c
artesian) product\, these systems constitute a lax symmetric monoidal func
tor from a category of interfaces (consisting of parameter and exposed var
iable sets) and coupling laws (often expressed as wiring diagrams) to the
category of sets --- that is\, we have a symmetric monoidal right module o
f systems over the symmetric monoidal category of interfaces and coupling
laws. Schultz\, Spivak and Vasilakopoulou show that the behavior of these
systems may be expressed as a morphism of lax symmetric monoidal functors
from this module of systems to a module of time-varying sets --- sheaves o
n the interval domain of the real line.\n\nIn this talk\, we'll see that t
he SSV behavior functors --- and many others similar behavior functors ---
are in fact representable when seen not as concerning right modules of ca
tegories\, but as concerning right modules over double categories. We will
develop the theory of (loose) modules between double categories using an
approach inspired by Joyal's "barrels" (joint work with Sophie Libkind)\,
and describe the cartesian pseudo-functoriality of restriction of loose ri
ght modules which allows for the pseudo-functorial construction of symmetr
ic monoidal loose right modules of open dynamical systems from an abstract
notion of "tangent bundle category". By expanding the definition of "tang
ent bundle" in this way\, we include all sorts of generalized Moore machin
es (including not only systems of ordinary differential equations\, but al
so partially observable Markov processes and various sorts of non-determin
istic automata).\n\nWe'll then see a general result (joint work with Matte
o Capucci) giving conditions under which discrete opfibration classifiers
in a 2-category K can be lifted to the 2-category of algebras and lax morp
hisms for a 2-monad T on K. We will use this result to show that a certain
symmetric monoidal loose right module of spans is a discrete opfibration
classifier among symmetric monoidal loose right modules\, and conclude by
showing that a variety of behavior functors for open dynamical systems are
covariantly representable. Time permitting\, we will also see that system
safety and stability properties are often themselves contravariantly repr
esentable via the representability of Lyapunov and control barrier functio
ns by functions into simple systems.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer (UT Dallas)
DTSTART:20250530T113000Z
DTEND:20250530T123000Z
DTSTAMP:20260424T221812Z
UID:BilTop/116
DESCRIPTION:Title: Topological Machine Learning\nby Baris Coskunuzer (UT Dallas)
as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract
\nIn this talk\, we will explore key techniques in topological machine lea
rning and highlight their applications in two distinct areas. First\, we w
ill discuss computer-aided drug discovery\, where Multiparameter Persisten
ce is leveraged for graph representation learning. Second\, we will examin
e cancer detection from histopathological images using cubical persistence
. Our approach is applied to five different cancer types\, achieving super
ior performance compared to state-of-the-art deep learning methods. The ta
lk is designed to be accessible for advanced undergraduate students in mat
hematics\, science\, and engineering\, requiring no prior knowledge of top
ology or machine learning.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Jan Mikhail (University of Copenhagen)
DTSTART:20250707T103000Z
DTEND:20250707T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/117
DESCRIPTION:Title: Abacus bicomodule configurations and the Bergner–Osorno–Ozorno
va–Rovelli–Scheimbauer equivalence\nby Thomas Jan Mikhail (Univers
ity of Copenhagen) as part of Bilkent Topology Seminar\n\nLecture held in
SA 141.\n\nAbstract\nA theorem of Bergner\, Osorno\, Ozornova\, Rovelli\,
and Scheimbauer states an equivalence between 2-Segal spaces and certain a
ugmented stable double Segal spaces. In this talk\, after a preliminary se
ction on 2-Segal spaces\, I will establish more general equivalences\, inv
olving simplicial maps of 2-Segal spaces and abacus bicomodule configurati
ons\, extending results of Carlier. This talk is based on joint work with
Joachim Kock\, and a preprint of this work is available on the arXiv (see
arXiv:2501.16491).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Ping Lai (Oregon State University)
DTSTART:20250709T103000Z
DTEND:20250709T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/118
DESCRIPTION:Title: Homology of Simplicial G-complexes and Group Rings\nby Chung-P
ing Lai (Oregon State University) as part of Bilkent Topology Seminar\n\nL
ecture held in SA 141.\n\nAbstract\nThere has been a growing trend to use
the homology of simplicial complexes to study complex data structures beca
use of its resilience to deformation and noise. In this talk\, we investi
gate the question of how one can recover the homology of a simplicial comp
lex X equipped with a regular action of a finite group G from the structur
e of its quotient space X/G. Specifically\, we describe a process for enri
ching the structure of the chain complex C*(X/G\; F) using the data of a c
omplex of groups\, a framework developed by Bridson and Corsen for encodin
g the local structure of a group action. We interpret this data through th
e lens of matrix representations of the acting group\, and combine this st
ructure with the standard simplicial boundary matrices for X/G to construc
t a surrogate chain complex. In the case G = Zk\, the group ring FG is com
mutative and matrices over FG admit a Smith normal form\, allowing us to r
ecover the homology of G from this surrogate complex. This algebraic appro
ach complements the geometric compression algorithm for equivariant simpli
cial complexes described by Carbone\, Nanda\, and Naqvi.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Basak Kucuk (University of Göttingen)
DTSTART:20250711T103000Z
DTEND:20250711T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/119
DESCRIPTION:Title: The Conjecture of Klein and Williams for the Equivariant Fixed Poi
nt Problem\nby Basak Kucuk (University of Göttingen) as part of Bilke
nt Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nKlein and Will
iams developed an obstruction theory for the homotopical equivariant fixed
point problem\, which asks whether an equivariant map can be deformed\, t
hrough an equivariant homotopy\, to a map with no fixed points [KW\, Theor
em H]. An alternative approach was given by Fadell and Wong [FW]\, using a
collection of Nielsen numbers. The Nielsen number is a finer invariant th
an the Lefschetz number in the sense that it provides a converse to the Le
fschetz fixed point theorem. Klein and Williams [KW] conjectured that thes
e Nielsen numbers could be computed from their invariant.\nIn this talk\,
we present our findings on this conjecture by providing an explicit decomp
osition of the Klein–Williams invariant under the tom Dieck splitting. W
e further discuss the application of the equivariant fixed point problem t
o the periodic point problem of period n. In this setting\, we show that t
he Klein–Williams invariant and the Nielsen numbers N(fk)\, for all k di
viding n\, carry the same amount of information. However\, they are not ex
actly the same invariants\, and if time permits\, we will conclude with an
explicit example illustrating this difference.\nReferences:\n[KW] J. R.
Klein and B. Williams\, Homotopical intersection theory II\, Math. Z. 264
(2010).\n[FW] E. Fadell and P. Wong\, On deforming G-maps to be fixed poi
nt free\, Pacific Journal of Mathematics 132 (1988).\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20251006T123000Z
DTEND:20251006T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/120
DESCRIPTION:Title: Free Actions on Products of Real Projective Spaces\nby Ergun Y
alcin (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture
held in SA 141.\n\nAbstract\nWe recently proved the homotopy-theoretical v
ersion of a conjecture\nby Cusick from 1983 on free actions of elementary
abelian 2-groups on products\nof real projective spaces. In this talk I wi
ll explain the main ideas of the proof after\nintroducing the necessary ba
ckground.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20251013T123000Z
DTEND:20251013T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/121
DESCRIPTION:Title: The geometry of simplicial distributions on suspension scenarios\nby Aziz Kharoof (Bilkent University) as part of Bilkent Topology Semin
ar\n\nLecture held in SA 141.\n\nAbstract\nQuantum measurements often exhi
bit non-classical features\, such as contextuality\, which generalizes Bel
l's non-locality and serves as a resource in various quantum computation m
odels. Existing frameworks have rigorously captured these phenomena\, and
recently\, simplicial distributions have been introduced to deepen this un
derstanding. The geometrical structure of simplicial distributions can be
seen as a resource for applications in quantum information theory. In this
talk\, we use topological foundations to study this geometrical structure
\, leveraging the fact that\, in this simplicial framework\, measurements
and outcomes are represented as spaces. This allows us to depict contextua
lity as a topological phenomenon. We show that applying the cone construct
ion to the measurement space makes the corresponding non-signaling polytop
e equal to the join of m copies of the original polytope\, where m is the
number of possible outcomes per measurement. Then we glue two copies of co
ne measurement spaces to obtain a suspension measurement space. The decomp
osition done for simplicial distributions on a cone measurement space prov
ides deeper insights into the geometry of simplicial distributions on a su
spension measurement space and aids in characterizing the contextuality th
ere. Additionally\, we apply these results to derive a new type of Bell in
equalities (inequalities that determine the set of local joint probabiliti
es/non-contextual simplicial distributions) and to offer a mathematical ex
planation for certain contextual vertices from the literature.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Ping Lai (Bilkent University)
DTSTART:20251020T123000Z
DTEND:20251020T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/122
DESCRIPTION:Title: Reducing Complexes with Discrete Morse Theory\nby Chung-Ping L
ai (Bilkent University) as part of Bilkent Topology Seminar\n\nLecture hel
d in SA 141.\n\nAbstract\nSimplicial decompositions of spaces often introd
uce large number of simplices which can become a nuisance especially in co
mputational settings. Inspired by smooth Morse theory\, Forman introduced
discrete Morse theory which\, among its many applications\, offers an appr
oach to reduce many kinds of cell complexes. In this talk we first introdu
ce an abstract cell complex that unifies various combinatorial spaces—su
ch as simplicial and CW complexes. We then show how discrete Morse theory
allows us to reduce a finite cell complex to a Morse complex which contain
s less cells while preserving the homology.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chung-Ping Lai (Oregon State University)
DTSTART:20251027T123000Z
DTEND:20251027T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/123
DESCRIPTION:Title: Persistent Homology and Discrete Morse Theory\nby Chung-Ping L
ai (Oregon State University) as part of Bilkent Topology Seminar\n\nLectur
e held in SA 141.\n\nAbstract\nPersistent homology is a powerful tool in a
pplied topology\, yet its computation can be expensive. In this talk we wi
ll briefly introduce persistent homology. Then\, building on our previous
discussion of Discrete Morse Theory (DMT)\, we demonstrate how DMT can be
used to reduce the size of relevant complexes in persistent homology\, lea
ding to gains in computational efficiency.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron David Fairbanks (Dalhousie University)
DTSTART:20251103T123000Z
DTEND:20251103T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/124
DESCRIPTION:Title: Comonads on Set\nby Aaron David Fairbanks (Dalhousie Universit
y) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstr
act\nIt was noticed only within the last decade that polynomial comonads o
n Set are small categories. What then are general comonads on Set? Joint w
ork with Kevin Carlson and David Spivak.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin M. Curry (University at Albany)
DTSTART:20251110T130000Z
DTEND:20251110T140000Z
DTSTAMP:20260424T221812Z
UID:BilTop/125
DESCRIPTION:Title: Stratification Theory for Reinforcement Learning\nby Justin M.
Curry (University at Albany) as part of Bilkent Topology Seminar\n\nLectu
re held in SA 141.\n\nAbstract\nIn this talk I will use the framework of p
oset-stratified spaces to study games\, where reward can be both discrete
and continuous. Following work by Yuliy Baryshnikov\, I will show how cert
ain video games naturally give rise to stratified spaces. Surprisingly\, w
hen modern neural nets are trained to play these same video games\, a simi
lar stratification structure can be observed in their latent representatio
ns. Our methods follow recent work by Michael Robinson and others on using
Volume Growth Laws to detect non-manifold structure in the token space fo
r LLMs. We expand and strengthen Robinson’s analysis by considering non-
textual data and prove a realization result for volume growth in a stratif
ied space. This is joint work with Brennan Lagasse\, Ngoc B. Lam\, Gregory
Cox\, David Rosenbluth\, and Alberto Speranzon.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Moeller (Caltech)
DTSTART:20251124T160000Z
DTEND:20251124T170000Z
DTSTAMP:20260424T221812Z
UID:BilTop/127
DESCRIPTION:Title: Hybrid dynamical systems as coalgebras\nby Joe Moeller (Caltec
h) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstr
act\nLyapunov theory provides a method for certifying the stability of a d
ynamical system without solving infeasible systems of differential equatio
ns. This theory has practical implications in the design of control algori
thms for many sorts of systems including robotics. We present a categorica
l framework for Lyapunov stability theory. This theory is developed in the
language of coalgebras\, where a system is viewed as a coalgebra of an en
dofunctor. Examples include continuous dynamical systems as coalgebras of
the tangent bundle functor\, and discrete transition systems as coalgebras
of the powerset functor. We blend these two standard examples to give a c
oalgebraic encoding of hybrid dynamical systems\, which appear naturally i
n engineering contexts such as robotic bipedal locomotion. This enables us
to apply the categorical Lyapunov theory to hybrid systems and find new c
onditions for certifying the stability of Zeno equilibria.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20251201T123000Z
DTEND:20251201T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/128
DESCRIPTION:Title: [cancelled] Simplicial methods in the resource theory of contextua
lity\nby Aziz Kharoof (Bilkent University) as part of Bilkent Topology
Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, we introdu
ce two categories:\nThe category of event scenarios\, which extends the st
andard scenarios known from the sheaf-theoretic approach.\nThe category of
scenarios over a monad with a gluing operation\, which extends the catego
ry of simplicial bundle scenarios.\nWe define the empirical model and simp
licial distribution functors for these categories using the relative Groth
endieck construction that presented in Behzat’s talk. We then introduce
an internal hom structure for event scenarios and for simplicial bundle sc
enarios\, which we call mapping scenarios.\nFinally\, we present our main
result\, which characterizes convex maps between simplicial distributions
in terms of non-contextual distributions on the corresponding mapping scen
ario\, thereby enhancing and extending previous results in categorical qua
ntum foundations.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Tombari (KTH - Royal Institute of Technology)
DTSTART:20251208T123000Z
DTEND:20251208T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/129
DESCRIPTION:Title: Decompositions of tame parametrised chain complexes\nby France
sca Tombari (KTH - Royal Institute of Technology) as part of Bilkent Topol
ogy Seminar\n\nLecture held in SA 141.\n\nAbstract\nWe show a classificati
on result for tame filtered chain complexes with indexing posets of dimens
ion 1. Filtered chain complexes\, on the one hand\, arise from filtrations
of finite point clouds. On the other hand\, they are the cofibrant replac
ements of any tame parametrised chain complex\, once an appropriate model
category structure is defined. Posets of dimension 1 form the other fundam
ental piece of this presentation. Examples of these are given by natural\,
integer\, real numbers with the usual order\, trees and zigzags. \n\nOur
classification result states that there are only two types of cofibrant (f
iltered) indecomposables in the category tame(Q\, ch(C))\, where Q is a po
set of dimension 1\, and C is an appropriate category. They are either dis
ks (trivial homology) of indecomposable projectives in tame(Q\, C) or sphe
res (non-trivial homology) on the minimal projective resolution of the hom
ology of the chain complex. Both of them are nonzero in only two consecuti
ve degrees. If time allows\, we will also show a technique\, based on “g
lueing”\, to construct indecomposables in a functor category by “small
er” indecomposables. Examples obtained in this way will also show that t
he results presented above\, for functors indexed by posets of dimension 1
\, are not immediately generalisable. \n\nThis presentation is based on jo
int work with Wojciech Chachólski\, Barbara Giunti and Claudia Landi.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Urs Schreiber (NYU Abu Dhabi)
DTSTART:20251215T123000Z
DTEND:20251215T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/130
DESCRIPTION:Title: Fragile Topological Phases and Topological Order of 2D Crystalline
Chern Insulators\nby Urs Schreiber (NYU Abu Dhabi) as part of Bilkent
Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nWe apply methods
of equivariant homotopy theory\, that may not previously have found due a
ttention in condensed matter physics\, to classify first the fragile topol
ogical phases of 2D crystalline Chern insulator materials\, and second the
potential topological order of their fractional cousins. We highlight tha
t the phases are given by the equivariant 2-Cohomotopy of the Brillouin to
rus of crystal momenta (with respect to wallpaper point group actions) —
which\, despite the attention devoted to crystalline Chern insulators\, s
eems not to have been considered before. Arguing then that any topological
order must be reflected in the adiabatic monodromy of gapped quantum grou
nd states over the covariantized moduli space of these band topologies\, w
e compute the latter in various examples where this group is non-abelian\,
should that potential anyons must be localized in momentum space. We clos
e with an outlook on the relevance for the search for topological quantum
computing hardware.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjørnar Gullikstad Hem (EPFL)
DTSTART:20251222T123000Z
DTEND:20251222T133000Z
DTSTAMP:20260424T221812Z
UID:BilTop/131
DESCRIPTION:Title: Decomposing multipersistence modules using functor calculus\nb
y Bjørnar Gullikstad Hem (EPFL) as part of Bilkent Topology Seminar\n\nLe
cture held in SA 141.\n\nAbstract\nMultiparameter persistent homology has
attracted growing interest in the topological data analysis community\, in
part due to its ability to handle noisy data. However\, unlike the single
-parameter case\, multipersistence modules do not generally admit an inter
val decomposition\, which makes the multiparameter setting considerably mo
re complicated. Nevertheless\, there exist certain sufficient conditions t
hat guarantee interval decomposability\, such as a locally defined conditi
on called middle exactness.\nIn this talk\, I introduce poset cocalculus\,
which is a variant of functor (co)calculus that is defined for functors f
rom a poset to a model category. The motivation for this framework lies in
the relevance of functors from posets to the model category of chain comp
lexes over a field\, as any multipersistence module is the homology of suc
h a functor. Poset cocalculus provides tools for relating local conditions
on these functors to their global structure. I apply this to give a novel
\, more synthetic proof of the fact that middle exactness implies interval
decomposability.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Shulman (University of San Diego)
DTSTART:20260323T160000Z
DTEND:20260323T170000Z
DTSTAMP:20260424T221812Z
UID:BilTop/132
DESCRIPTION:Title: Doubly weak double categories\nby Michael Shulman (University
of San Diego) as part of Bilkent Topology Seminar\n\nLecture held in SA 14
1.\n\nAbstract\nDouble categories are a two-dimensional categorical struct
ure with two different classes of 1-cells\, and 2-cells shaped like a squa
re. It is easy to define double categories with strict composition like 2
-categories\; but double categories with weak composition analogous to bic
ategories\, for both kinds of 1-cells\, are surprisingly difficult to defi
ne. We give a simple definition of "doubly weak double categories" by usi
ng the notion of "implicit" categorical structure\, in which composition i
s not an algebraic operation at all but is witnessed by isomorphisms. The
n we discuss various ways in which this can be made algebraic. This is jo
int work with Aaron David Fairbanks.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ergun Yalcin (Bilkent University)
DTSTART:20260330T103000Z
DTEND:20260330T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/133
DESCRIPTION:Title: Worst-case examples for the computation of persistent homology
\nby Ergun Yalcin (Bilkent University) as part of Bilkent Topology Seminar
\n\nLecture held in SA 141.\n\nAbstract\nTopological Data Analysis via per
sistent homology is a new emerging area of data analysis that uses method
s from simplicial topology. The persistent homology of a data set can be c
alculated using a simple algorithm called reduction algorithm. In this
talk\, I will present a new construction of worst-case examples for this
algorithm. Our constructions are similar to the worst-case examples introd
uced by Morozov\, but replace the single-triangle arrangement with a stri
p formed by base and fin triangles. This structure allows us to give an e
xplicit algorithm for their construction and to perform experiments compar
ing the runtime of different variants of the reduction algorithm. We fu
rther show that\, after suitable edge and triangle subdivisions\,\nthese s
trip examples remain worst-case and can be realized as clique complexes of
filtered graphs\, and hence as Vietoris--Rips complexes of finite point
clouds for a sequence of scale parameters.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20260406T103000Z
DTEND:20260406T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/134
DESCRIPTION:Title: Extremal Simplicial Distributions on Glued Measurement Spaces\
nby Aziz Kharoof (Bilkent University) as part of Bilkent Topology Seminar\
n\nLecture held in SA 141.\n\nAbstract\nSimplicial distributions form the
Kleisli category of the distribution monad on simplicial sets. They were i
ntroduced as a framework for studying non-signaling polytopes and contextu
ality arising from measurements in quantum physics\, with applications in
quantum information theory. The domain of a simplicial distribution is a s
implicial set that encodes the compatible measurements in a given scenario
and is called the measurement space.\n\nIn this talk\, we characterize ex
tremal simplicial distributions when the measurement space is a colimit of
a diagram of simplicial sets. We apply this result to cases in which iden
tical spaces are glued together along a common subspace. In particular\, w
e obtain a characterization of extremal simplicial distributions on what w
e call the rose and dipole graphs. Finally\, we show how this characteriza
tion can be used to detect extremal simplicial distributions on one-dimens
ional measurement spaces.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Frankland (University of Regina)
DTSTART:20260413T103000Z
DTEND:20260413T113000Z
DTSTAMP:20260424T221812Z
UID:BilTop/135
DESCRIPTION:Title: Enriched model categories and the Dold-Kan correspondence\nby
Martin Frankland (University of Regina) as part of Bilkent Topology Semina
r\n\nLecture held in SA 141.\n\nAbstract\nIf we start with a model categor
y enriched in simplicial abelian groups and we normalize each hom complex\
, what kind of structure do we obtain? In joint work with Arnaud Ngopnang
Ngompé\, we show that changing the enrichment along a weak monoidal Quill
en pair results in a "weak" enriched model category. The main issue is tha
t we lose the tensoring and cotensoring\, but we retain a weak form thereo
f.\n
LOCATION:https://stable.researchseminars.org/talk/BilTop/135/
END:VEVENT
END:VCALENDAR